[{"data":1,"prerenderedAt":991},["ShallowReactive",2],{"questions:data-handling":3},{"bank":4,"contentHash":982,"dependencyHashes":983,"releaseId":990},{"schemaVersion":5,"conceptId":6,"revision":5,"title":7,"intro":8,"sections":9,"questions":46,"sourceIds":972,"reviewStatus":978,"authoring":979},1,"data-handling","Data handling question bank","Questions on collecting and organising data, tally marks and frequency tables, pictographs, bar graphs and pie charts, and the four summaries: mean, median, mode and range. They grow from **foundation** (one step) through **core** and **stretch** to **challenge** (olympiad-style reasoning). Every question has a worked solution; try it yourself before opening it. Tip for many averages problems: switch from the mean to the **total**, because sum = mean × count.",[10,14,18,22,26,30,34,38,42],{"id":11,"title":12,"description":13},"collecting","Collecting and organising data","Surveys, observation and measurement; fair questions; kinds of data; samples and privacy.",{"id":15,"title":16,"description":17},"tally","Tally marks and frequency tables","Counting with tally marks, building and reading frequency tables, and grouping data into class intervals.",{"id":19,"title":20,"description":21},"graphs","Pictographs, bar graphs and pie charts","Keys and scales, reading and comparing bars, pie-chart angles, and misleading graphs.",{"id":23,"title":24,"description":25},"mean","Mean","Sum ÷ count, means from frequency tables, properties of the mean and combined means.",{"id":27,"title":28,"description":29},"median","Median","The middle of ordered data, odd and even counts, and medians from frequency tables.",{"id":31,"title":32,"description":33},"mode","Mode","The most frequent value, two modes, no mode, categorical data and modal class.",{"id":35,"title":36,"description":37},"range","Range","Spread as maximum − minimum, consistency, and how shifting or scaling affects the range.",{"id":39,"title":40,"description":41},"choosing","Choosing an average and outliers","Which average suits a situation, outliers, batting averages and average speed.",{"id":43,"title":44,"description":45},"reasoning","Missing values and reasoning","Recovering missing values from a mean, correcting errors, and multi-step puzzles.",[47,72,91,107,126,146,162,175,193,205,222,232,242,250,259,269,279,288,297,306,315,334,351,361,372,382,391,400,410,419,430,440,449,459,469,479,487,497,506,516,534,542,551,560,567,577,595,613,621,639,659,668,675,683,693,711,720,728,746,755,769,786,795,806,823,834,844,852,870,878,885,894,903,913,922,929,938,947,955,964],{"id":48,"section":11,"level":49,"prompt":50,"check":51,"hints":67,"solution":69,"skills":70},"data-handling.q001","foundation","Rahul counts the number of cars, buses and two-wheelers passing his gate in 15 minutes. Which method of collecting data is he using?",{"kind":52,"options":53,"correct":66},"choice",[54,57,60,63],{"id":55,"label":56},"a","Survey",{"id":58,"label":59},"b","Observation",{"id":61,"label":62},"c","Measurement",{"id":64,"label":65},"d","Questionnaire",[58],[68],"Is Rahul asking anyone a question?","He is **watching and counting** without asking anyone anything, so it is an **observation**. A survey or questionnaire would mean asking people; a measurement would need a tool such as a ruler or thermometer.",[71],"collecting data",{"id":73,"section":11,"level":49,"prompt":74,"check":75,"hints":86,"solution":88,"skills":89},"data-handling.q002","Which of these survey questions is **fair** (does not push people towards an answer)?",{"kind":52,"options":76,"correct":85},[77,79,81,83],{"id":55,"label":78},"Don't you think cricket is the best sport?",{"id":58,"label":80},"Which sport do you like most: cricket, football, kabaddi, badminton or another?",{"id":61,"label":82},"Football is boring, isn't it?",{"id":64,"label":84},"Why do you dislike kho-kho?",[58],[87],"Look for words that suggest what the answer \"should\" be.","Option b gives every choice (including \"another\") and does not suggest a right answer. The others all push the person: a and c suggest an opinion, and d assumes the person dislikes kho-kho.",[90],"fair questions",{"id":92,"section":11,"level":49,"prompt":93,"check":94,"hints":103,"solution":104,"skills":105},"data-handling.q003","Is this statement true or false? \"The number of siblings a child has is categorical data.\"",{"kind":52,"options":95,"correct":102},[96,99],{"id":97,"label":98},"t","True",{"id":100,"label":101},"f","False",[100],[],"False. The number of siblings is **numerical** data. You count it (0, 1, 2, …) and adding or averaging makes sense. It is **discrete** because only whole numbers are possible.",[106],"kinds of data",{"id":108,"section":11,"level":109,"prompt":110,"check":111,"hints":122,"solution":124,"skills":125},"data-handling.q004","core","Which of these is **continuous** numerical data?",{"kind":52,"options":112,"correct":121},[113,115,117,119],{"id":55,"label":114},"Number of goals in a match",{"id":58,"label":116},"Blood group",{"id":61,"label":118},"Time taken to walk to school",{"id":64,"label":120},"Number of pages in a book",[61],[123],"Could a value like 12.47 make sense?","Time is **measured** and can take any value (12.5 minutes, 12.47 minutes…), so it is continuous. Goals and pages are counted (discrete), and blood group is categorical.",[106],{"id":127,"section":11,"level":109,"prompt":128,"check":129,"hints":140,"solution":142,"skills":143},"data-handling.q005","A student wants to know the favourite snack of the **whole school** of 600 children. She asks only the 8 members of her dance club. What is wrong with her sample?",{"kind":52,"options":130,"correct":139},[131,133,135,137],{"id":55,"label":132},"Too small only",{"id":58,"label":134},"Biased only",{"id":61,"label":136},"Both too small and biased",{"id":64,"label":138},"There is no problem",[61],[141],"Would the dance club be like the whole school?","Eight children is a tiny sample of 600, and they are not chosen fairly: members of one club are likely to share tastes and are not representative of the school. So the sample is **both too small and biased**. A better plan: ask a larger group chosen fairly from every class, for example by drawing roll numbers.",[144,145],"sampling","bias",{"id":147,"section":11,"level":109,"prompt":148,"check":149,"hints":158,"solution":160,"skills":161},"data-handling.q006","Is a cricket player's jersey number numerical or categorical data?",{"kind":52,"options":150,"correct":157},[151,153,155],{"id":55,"label":152},"Numerical, discrete",{"id":58,"label":154},"Numerical, continuous",{"id":61,"label":156},"Categorical",[61],[159],"Does adding jersey numbers make sense?","A jersey number is a **label**, even though it is written with digits. Jersey 18 is not \"twice\" jersey 9, and the mean of jersey numbers means nothing. So it is **categorical**.",[106],{"id":163,"section":11,"level":164,"prompt":165,"check":166,"hints":170,"solution":172,"skills":173},"data-handling.q007","stretch","Rainfall figures that you copy from the India Meteorological Department website are called ____ data. (Type one word.)",{"kind":167,"accept":168},"text",[169],"secondary",[171],"Did you collect it yourself?","**Secondary** data is collected by someone else and reused by you. If you measured rainfall yourself with a rain gauge, it would be **primary** data.",[174],"primary and secondary",{"id":176,"section":11,"level":164,"prompt":177,"check":178,"hints":189,"solution":190,"skills":191},"data-handling.q008","A class survey asks: \"Write your name, your home address and your favourite game.\" Which part of the survey should be removed to protect privacy while still answering the question \"What is the class's favourite game?\"",{"kind":52,"options":179,"correct":188},[180,182,184,186],{"id":55,"label":181},"Favourite game",{"id":58,"label":183},"Name and home address",{"id":61,"label":185},"Only the name",{"id":64,"label":187},"Nothing; all of it is needed",[58],[],"To find the most popular game you only need each person's favourite game. Names and addresses are **personal data** that the question does not need, so they should not be collected. Collect only what you need.",[192],"data ethics",{"id":194,"section":15,"level":49,"prompt":195,"check":196,"hints":200,"solution":202,"skills":203},"data-handling.q009","What number does this tally show? 卌 卌 卌 卌 ||| (each 卌 is a gate of 5)",{"kind":197,"answer":198,"tolerance":199},"number",23,0,[201],"Count the gates in fives first.","Four gates of 5 make 20. Three single strokes make 3 more. 20 + 3 = **23**.",[204],"tally marks",{"id":206,"section":15,"level":49,"prompt":207,"check":208,"hints":219,"solution":220,"skills":221},"data-handling.q010","How many complete gates (groups of 5) and how many single strokes do you draw to tally 17?",{"kind":52,"options":209,"correct":218},[210,212,214,216],{"id":55,"label":211},"3 gates and 2 strokes",{"id":58,"label":213},"1 gate and 7 strokes",{"id":61,"label":215},"17 strokes",{"id":64,"label":217},"2 gates and 7 strokes",[55],[],"17 = 5 + 5 + 5 + 2, so **3 gates and 2 single strokes**. Each gate is 4 upright strokes crossed by a fifth.",[204],{"id":223,"section":15,"level":49,"prompt":224,"check":225,"hints":227,"solution":229,"skills":230},"data-handling.q011","Twelve children named their favourite fruit: mango, apple, mango, banana, mango, guava, apple, mango, banana, mango, apple, guava. What is the frequency of mango?",{"kind":197,"answer":226,"tolerance":199},5,[228],"Cross off each word as you count it.","Count every \"mango\" in the list, crossing each off as you go: it appears **5** times. Check the whole table: mango 5, apple 3, banana 2, guava 2; total 12 ✓.",[231],"frequency",{"id":233,"section":15,"level":109,"prompt":234,"check":235,"hints":237,"solution":239,"skills":240},"data-handling.q012","A frequency table for 40 students shows: walk 12, bus 15, cycle 7, car ?. How many come by car?",{"kind":197,"answer":236,"tolerance":199},6,[238],"The frequencies add up to the number of students.","The frequencies must add up to the total, 40. 12 + 15 + 7 = 34, so car = 40 − 34 = **6**.",[241],"frequency table",{"id":243,"section":15,"level":109,"prompt":244,"check":245,"hints":246,"solution":248,"skills":249},"data-handling.q013","A die was rolled 20 times: 3, 5, 2, 6, 5, 1, 4, 5, 3, 6, 2, 5, 4, 1, 5, 6, 3, 5, 2, 4. Make a frequency table. How many times did 5 come up?",{"kind":197,"answer":236,"tolerance":199},[247],"Go through the list once, making a stroke for each value.","Tally each face once through the list: 1 → 2, 2 → 3, 3 → 3, 4 → 3, 5 → **6**, 6 → 3. Check: 2 + 3 + 3 + 3 + 6 + 3 = 20 ✓.",[241],{"id":251,"section":15,"level":109,"prompt":252,"check":253,"hints":255,"solution":257,"skills":258},"data-handling.q014","In a class, the number of siblings has these frequencies: 0 siblings: 5 children, 1: 14, 2: 8, 3: 2, 4: 1. How many children have **at least 2** siblings?",{"kind":197,"answer":254,"tolerance":199},11,[256],"At least 2 includes 2.","\"At least 2\" means 2, 3 or 4 siblings: 8 + 2 + 1 = **11** children.",[241],{"id":260,"section":15,"level":164,"prompt":261,"check":262,"hints":264,"solution":266,"skills":267},"data-handling.q015","Using the siblings table (0: 5, 1: 14, 2: 8, 3: 2, 4: 1), how many siblings do all the children have altogether?",{"kind":197,"answer":263,"tolerance":199},40,[265],"Each child with 2 siblings contributes 2.","Multiply each value by its frequency and add: 0 × 5 + 1 × 14 + 2 × 8 + 3 × 2 + 4 × 1 = 0 + 14 + 16 + 6 + 4 = **40** siblings.",[241,268],"f × x",{"id":270,"section":15,"level":164,"prompt":271,"check":272,"hints":274,"solution":276,"skills":277},"data-handling.q016","Marks out of 50: 23, 45, 38, 12, 49, 31, 27, 40, 35, 18, 44, 29, 33, 20, 41. Grouping them in class intervals 10–20, 20–30, 30–40, 40–50 (lower limit included, upper limit excluded), what is the frequency of the class 30–40?",{"kind":197,"answer":273,"tolerance":199},4,[275],"Is 40 in 30–40 or 40–50?","Marks with 30 ≤ mark \u003C 40 are 38, 31, 35 and 33: **4** marks. (40 goes into 40–50, because each interval includes its lower limit and excludes its upper limit.)",[278],"grouped data",{"id":280,"section":15,"level":281,"prompt":282,"check":283,"hints":284,"solution":286,"skills":287},"data-handling.q017","challenge","A tally sheet for 50 votes was torn. The visible counts are: Priya 卌 卌 卌 |, Arjun 卌 卌 卌 卌 ||, and the rest went to Meena. Meena says she won. Is she right, and by how many votes did the winner beat the second-placed candidate?",{"kind":197,"answer":236,"tolerance":199},[285],"Find each candidate's total; Meena's is what is left of 50.","Priya: 15 + 1 = 16. Arjun: 20 + 2 = 22. Meena: 50 − 16 − 22 = 12. **Arjun** won, not Meena. Arjun beat Priya by 22 − 16 = **6** votes.",[204,43],{"id":289,"section":19,"level":49,"prompt":290,"check":291,"hints":293,"solution":294,"skills":295},"data-handling.q018","In a pictograph the key is ⚽ = 6 children. How many children does a row of ⚽⚽⚽⚽ show?",{"kind":197,"answer":292,"tolerance":199},24,[],"4 symbols × 6 children = **24** children. Always read the key.",[296],"pictographs",{"id":298,"section":19,"level":49,"prompt":299,"check":300,"hints":302,"solution":304,"skills":305},"data-handling.q019","In a pictograph, 🍎 = 10 apples. How many symbols are needed to show 35 apples?",{"kind":197,"answer":301,"tolerance":199},3.5,[303],"Divide by the key.","35 ÷ 10 = **3.5**: three full apples and one half apple.",[296],{"id":307,"section":19,"level":109,"prompt":308,"check":309,"hints":311,"solution":312,"skills":313},"data-handling.q020","A bar graph of books read in a month by five friends has these bar heights: Anu 12, Bala 8, Chetan 15, Divya 10, Esha 5. Chetan read how many times as many books as Esha?",{"kind":197,"answer":310,"tolerance":199},3,[],"15 ÷ 5 = **3** times. Bar graphs make such comparisons quick when the axis starts at 0.",[314],"bar graphs",{"id":316,"section":19,"level":109,"prompt":317,"check":318,"hints":329,"solution":331,"skills":332},"data-handling.q021","The largest value to be shown on a bar graph is 850 and there are 10 squares on the value axis. Which scale is most sensible?",{"kind":52,"options":319,"correct":328},[320,322,324,326],{"id":55,"label":321},"1 square = 10",{"id":58,"label":323},"1 square = 50",{"id":61,"label":325},"1 square = 100",{"id":64,"label":327},"1 square = 500",[61],[330],"Divide 850 by each scale.","With 1 square = 100, 850 needs 8.5 squares, which fits in 10. With 1 square = 50 it needs 17 squares (too many); with 1 square = 500 the bars would be less than 2 squares tall and hard to compare.",[314,333],"scale",{"id":335,"section":19,"level":109,"prompt":336,"check":337,"hints":348,"solution":349,"skills":350},"data-handling.q022","Which of these is a correct rule for drawing a bar graph?",{"kind":52,"options":338,"correct":347},[339,341,343,345],{"id":55,"label":340},"Bars can have different widths",{"id":58,"label":342},"The value axis should start at 0",{"id":61,"label":344},"Gaps between bars can be any size",{"id":64,"label":346},"You do not need a title",[58],[],"Only b is correct. Bars must have **equal widths** and **equal gaps**, so that only the height carries meaning, and the value axis should start at **0** so bar lengths are in proportion to the values. Every graph needs a title.",[314],{"id":352,"section":19,"level":164,"prompt":353,"check":354,"hints":356,"solution":358,"skills":359},"data-handling.q023","A pie chart shows how 120 students come to school. The \"bus\" sector has an angle of 150°. How many students come by bus?",{"kind":197,"answer":355,"tolerance":199},50,[357],"What fraction of 360° is 150°?","Fraction of the circle = 150 ÷ 360 = 5\u002F12. Students = 5\u002F12 × 120 = **50**. Check: 50 ÷ 120 × 360° = 150° ✓.",[360],"pie charts",{"id":362,"section":19,"level":164,"prompt":363,"check":364,"hints":367,"solution":369,"skills":370},"data-handling.q024","In a family budget of ₹40,000, ₹6,000 is spent on transport. What angle should the transport sector have in a pie chart?",{"kind":197,"answer":365,"tolerance":199,"unit":366},54,"°",[368],"Angle = (part ÷ whole) × 360°.","6,000 ÷ 40,000 = 3\u002F20. 3\u002F20 × 360° = **54°**.",[360,371],"angles",{"id":373,"section":19,"level":164,"prompt":374,"check":375,"hints":377,"solution":379,"skills":380},"data-handling.q025","Two bars show 50 and 55. The value axis starts at 45 instead of 0. How many times taller does the second bar look than the first?",{"kind":197,"answer":376,"tolerance":199},2,[378],"Measure each bar from where the axis starts.","Above 45 the bars are 50 − 45 = 5 and 55 − 45 = 10 units tall, so the second looks **2** times as tall, though 55 is only 10% more than 50. This is the broken-axis trick.",[381],"misleading graphs",{"id":383,"section":19,"level":281,"prompt":384,"check":385,"hints":387,"solution":389,"skills":390},"data-handling.q026","A company's sales tripled. Its advertisement shows a picture of a shopping bag three times as tall and three times as wide as last year's. By what factor does the **area** of the picture grow?",{"kind":197,"answer":386,"tolerance":199},9,[388],"Area = width × height.","Area grows by 3 × 3 = **9**. The picture suggests sales grew nine-fold, three times the true growth. An honest picture would change only one dimension, or repeat same-size symbols.",[381],{"id":392,"section":23,"level":49,"prompt":393,"check":394,"hints":396,"solution":398,"skills":399},"data-handling.q027","Find the mean of 4, 8, 6, 10 and 7.",{"kind":197,"answer":395,"tolerance":199},7,[397],"Add them all, then divide by how many there are.","Sum = 4 + 8 + 6 + 10 + 7 = 35. Count = 5. Mean = 35 ÷ 5 = **7**.",[23],{"id":401,"section":23,"level":49,"prompt":402,"check":403,"hints":406,"solution":407,"skills":408},"data-handling.q028","Three friends have ₹20, ₹35 and ₹50. If they share the money equally, how much does each get?",{"kind":197,"answer":404,"tolerance":199,"unit":405},35,"₹",[],"20 + 35 + 50 = 105; 105 ÷ 3 = **₹35** each. This fair share is the mean.",[23,409],"fair share",{"id":411,"section":23,"level":109,"prompt":412,"check":413,"hints":416,"solution":417,"skills":418},"data-handling.q029","The maximum temperatures in Hyderabad for a week were 31, 33, 34, 36, 35, 32, 30 °C. Find the mean temperature.",{"kind":197,"answer":414,"tolerance":199,"unit":415},33,"°C",[],"Sum = 31 + 33 + 34 + 36 + 35 + 32 + 30 = 231. Mean = 231 ÷ 7 = **33 °C**.",[23],{"id":420,"section":23,"level":109,"prompt":421,"check":422,"hints":425,"solution":427,"skills":428},"data-handling.q030","Rainfall on seven days of a week was 0, 12, 25, 3, 0, 40, 18 mm. What was the mean daily rainfall?",{"kind":197,"answer":423,"tolerance":199,"unit":424},14,"mm",[426],"Zero-rain days are still days.","Sum = 98 mm over **7** days (the dry days count). Mean = 98 ÷ 7 = **14 mm**, even though it rained on only five of the days.",[23,429],"zeros count",{"id":431,"section":23,"level":109,"prompt":432,"check":433,"hints":436,"solution":438,"skills":439},"data-handling.q031","Twenty families were asked how many children they have: 1 child: 4 families, 2 children: 9, 3 children: 5, 4 children: 2. Find the mean number of children per family.",{"kind":197,"answer":434,"tolerance":435},2.25,0.001,[437],"Divide by the total number of families, 20.","Multiply each value by its frequency: 1 × 4 + 2 × 9 + 3 × 5 + 4 × 2 = 4 + 18 + 15 + 8 = 45. Total families = 20. Mean = 45 ÷ 20 = **2.25**.",[23,241],{"id":441,"section":23,"level":109,"prompt":442,"check":443,"hints":445,"solution":446,"skills":447},"data-handling.q032","The mean of 8 numbers is 12. What is their sum?",{"kind":197,"answer":444,"tolerance":199},96,[],"Sum = mean × count = 12 × 8 = **96**.",[448],"sum = mean × count",{"id":450,"section":23,"level":164,"prompt":451,"check":452,"hints":454,"solution":456,"skills":457},"data-handling.q033","A batter scored 45, 12, 78, 0, 33, 56 in six innings and was out every time. After a seventh innings the mean is 40. What did the batter score in the seventh innings?",{"kind":197,"answer":453,"tolerance":199},56,[455],"New total = new mean × 7.","Total after 7 innings = 40 × 7 = 280. Total of the first six = 224. Seventh innings = 280 − 224 = **56**.",[23,458],"missing value",{"id":460,"section":23,"level":164,"prompt":461,"check":462,"hints":464,"solution":466,"skills":467},"data-handling.q034","Every value in a data set with mean 18 is multiplied by 3 and then 4 is added. What is the new mean?",{"kind":197,"answer":463,"tolerance":199},58,[465],"Apply the same change to the mean.","Multiplying every value by 3 multiplies the mean: 18 × 3 = 54. Adding 4 to every value adds 4 to the mean: **58**.",[468],"properties of mean",{"id":470,"section":23,"level":281,"prompt":471,"check":472,"hints":474,"solution":476,"skills":477},"data-handling.q035","Section A has 25 students with mean mark 64. Section B has 35 students with mean mark 76. What is the mean mark of all 60 students?",{"kind":197,"answer":473,"tolerance":199},71,[475],"Work with totals, not averages.","Totals: 25 × 64 = 1,600 and 35 × 76 = 2,660. Together: 4,260 marks for 60 students. Mean = 4,260 ÷ 60 = **71**. (Not (64 + 76) ÷ 2 = 70: the bigger section counts for more.)",[478],"weighted mean",{"id":480,"section":27,"level":49,"prompt":481,"check":482,"hints":483,"solution":485,"skills":486},"data-handling.q036","Find the median of 7, 2, 9, 4, 5.",{"kind":197,"answer":226,"tolerance":199},[484],"Put them in order first.","Order: 2, 4, **5**, 7, 9. With 5 values the median is the 3rd: **5**.",[27],{"id":488,"section":27,"level":49,"prompt":489,"check":490,"hints":492,"solution":494,"skills":495},"data-handling.q037","Find the median of 3, 8, 6, 1.",{"kind":197,"answer":491,"tolerance":199},4.5,[493],"With an even count, take the mean of the two middle values.","Order: 1, 3, 6, 8. With 4 values there are two middle values, 3 and 6. Median = (3 + 6) ÷ 2 = **4.5**.",[27,496],"even count",{"id":498,"section":27,"level":109,"prompt":499,"check":500,"hints":503,"solution":504,"skills":505},"data-handling.q038","The heights of 9 players in a school basketball team are 142, 138, 150, 145, 139, 147, 141, 152, 144 cm. Find the median height.",{"kind":197,"answer":501,"tolerance":199,"unit":502},144,"cm",[],"Order: 138, 139, 141, 142, 144, 145, 147, 150, 152. With 9 values the median is the 5th: **144 cm**.",[27],{"id":507,"section":27,"level":109,"prompt":508,"check":509,"hints":512,"solution":514,"skills":515},"data-handling.q039","The number of minutes ten children spent reading yesterday: 12, 45, 7, 30, 22, 18, 40, 9, 25, 15. Find the median.",{"kind":197,"answer":510,"tolerance":199,"unit":511},20,"minutes",[513],"n = 10 is even.","Order: 7, 9, 12, 15, 18, 22, 25, 30, 40, 45. With 10 values, the median is the mean of the 5th and 6th: (18 + 22) ÷ 2 = **20 minutes**.",[27,496],{"id":517,"section":27,"level":109,"prompt":518,"check":519,"hints":530,"solution":531,"skills":532},"data-handling.q040","Riya found the median of 6, 1, 9, 4, 3 like this: \"The middle number is 9, so the median is 9.\" What mistake did she make?",{"kind":52,"options":520,"correct":529},[521,523,525,527],{"id":55,"label":522},"She did not put the numbers in order first",{"id":58,"label":524},"She should have added them",{"id":61,"label":526},"She should have used the mode",{"id":64,"label":528},"There is no mistake",[55],[],"She took the middle of the **unordered** list. In order the data is 1, 3, 4, 6, 9, so the median is **4**.",[27,533],"spot the mistake",{"id":535,"section":27,"level":164,"prompt":536,"check":537,"hints":538,"solution":540,"skills":541},"data-handling.q041","Quiz marks of 25 students: mark 5: 3 students, mark 6: 4, mark 7: 8, mark 8: 6, mark 9: 4. What is the median mark?",{"kind":197,"answer":395,"tolerance":199},[539],"Use a running total to find the 13th student.","n = 25, so the median is the 13th value. Running totals: 3 (mark 5), 7 (mark 6), 15 (mark 7), … The 13th student is within the mark-7 group (positions 8 to 15). Median = **7**.",[27,241],{"id":543,"section":27,"level":164,"prompt":544,"check":545,"hints":547,"solution":549,"skills":550},"data-handling.q042","The median of 5 different whole numbers is 12. The numbers are 7, 15, x, 20 and 9 in some order. What is x?",{"kind":197,"answer":546,"tolerance":199},12,[548],"Where must x go in the ordered list?","Ordered, the known numbers are 7, 9, 15, 20. For the middle (3rd) value to be 12, x must sit between 9 and 15 and be the median itself, so **x = 12**. Check: 7, 9, 12, 15, 20 → median 12 ✓.",[27,43],{"id":552,"section":27,"level":281,"prompt":553,"check":554,"hints":555,"solution":557,"skills":558},"data-handling.q043","Six numbers in order are 4, 7, a, b, 15, 20. Their median is 10 and b is 4 more than a. Find b, and then check that the mean is 11.",{"kind":197,"answer":546,"tolerance":199},[556],"With an even count, the median is the mean of the two middle values.","With six values the median is (a + b) ÷ 2 = 10, so a + b = 20. Since b = a + 4: a + a + 4 = 20, so a = 8 and **b = 12**. Check the order: 7 ≤ 8 ≤ 12 ≤ 15 ✓. Mean = (4 + 7 + 8 + 12 + 15 + 20) ÷ 6 = 66 ÷ 6 = 11 ✓.",[27,559],"algebra",{"id":561,"section":31,"level":49,"prompt":562,"check":563,"hints":564,"solution":565,"skills":566},"data-handling.q044","Find the mode of 3, 5, 5, 2, 8, 5, 3.",{"kind":197,"answer":226,"tolerance":199},[],"5 appears 3 times, 3 appears twice and the others once. Mode = **5**.",[31],{"id":568,"section":31,"level":49,"prompt":569,"check":570,"hints":573,"solution":574,"skills":575},"data-handling.q045","Favourite colours of a group: blue, red, green, blue, yellow, red, blue, green, blue. What is the mode?",{"kind":167,"accept":571},[572],"blue",[],"Blue appears 4 times, more than any other colour. Mode = **blue**. The mode is the only average that works for categories like colours.",[31,576],"categorical",{"id":578,"section":31,"level":109,"prompt":579,"check":580,"hints":591,"solution":592,"skills":593},"data-handling.q046","What is the mode of 12, 15, 17, 20, 23?",{"kind":52,"options":581,"correct":590},[582,584,586,588],{"id":55,"label":583},"17",{"id":58,"label":585},"23",{"id":61,"label":587},"There is no mode",{"id":64,"label":589},"12 and 23",[61],[],"Every value appears exactly once, so no value is more common than the others: there is **no mode**.",[31,594],"no mode",{"id":596,"section":31,"level":109,"prompt":597,"check":598,"hints":609,"solution":610,"skills":611},"data-handling.q047","What is the mode of 4, 7, 4, 9, 7, 2?",{"kind":52,"options":599,"correct":608},[600,602,604,606],{"id":55,"label":601},"4",{"id":58,"label":603},"7",{"id":61,"label":605},"4 and 7",{"id":64,"label":607},"No mode",[61],[],"4 and 7 each appear twice; 9 and 2 once. There are **two modes, 4 and 7** (the data is bimodal).",[31,612],"bimodal",{"id":614,"section":31,"level":109,"prompt":615,"check":616,"hints":617,"solution":619,"skills":620},"data-handling.q048","A shoe shop's sales table shows: size 5 sold 18 pairs, size 6 sold 31, size 7 sold 24, size 8 sold 9. What is the modal shoe size?",{"kind":197,"answer":236,"tolerance":199},[618],"Answer with the value, not how often it occurs.","The largest frequency is 31, for **size 6**. The mode is the size (6), not the frequency (31).",[31,241],{"id":622,"section":31,"level":164,"prompt":623,"check":624,"hints":635,"solution":636,"skills":637},"data-handling.q049","Grouped heights (cm): 120–130: 4 children, 130–140: 11, 140–150: 9, 150–160: 3. What is the modal class?",{"kind":52,"options":625,"correct":634},[626,628,630,632],{"id":55,"label":627},"120–130",{"id":58,"label":629},"130–140",{"id":61,"label":631},"140–150",{"id":64,"label":633},"150–160",[58],[],"The modal class is the interval with the highest frequency: **130–140** (11 children). With grouped data you name a class, not an exact mode.",[638,278],"modal class",{"id":640,"section":31,"level":164,"prompt":641,"check":642,"hints":655,"solution":657,"skills":658},"data-handling.q050","The data 3, 6, 6, 8, 9 has one mode, 6. Which single numbers could you add to make the data have **exactly two** modes? Select all that work.",{"kind":52,"options":643,"correct":654},[644,646,648,649,651],{"id":55,"label":645},"3",{"id":58,"label":647},"6",{"id":61,"label":603},{"id":64,"label":650},"8",{"id":652,"label":653},"e","9",[55,64,652],[656],"Which values appear only once now?","Now 6 appears twice and 3, 8, 9 once each. Adding **3, 8 or 9** makes that value appear twice too, tying with 6: two modes. Adding 6 makes 6 appear three times (still one mode). Adding 7 adds a new value that appears once (still one mode, 6).",[31,612],{"id":660,"section":31,"level":281,"prompt":661,"check":662,"hints":663,"solution":665,"skills":666},"data-handling.q051","Five positive whole numbers have mean 6, median 6 and a single mode 9. What is the least possible value of the smallest number?",{"kind":197,"answer":5,"tolerance":199},[664],"Place 6 in the middle and the two 9s at the top.","Order a ≤ b ≤ c ≤ d ≤ e. Median c = 6. Mode 9 must appear at least twice and be above 6, so d = e = 9. Total = 30, so a + b = 30 − 6 − 18 = 6. Options: (1, 5), (2, 4) or (3, 3). (3, 3) makes 3 a second mode, so it is not allowed. Both (1, 5) and (2, 4) work, so the smallest number could be 1 or 2; the smallest **possible** value is **1** (data 1, 5, 6, 9, 9).",[31,23,667],"puzzle",{"id":669,"section":35,"level":49,"prompt":670,"check":671,"hints":672,"solution":673,"skills":674},"data-handling.q052","Find the range of 14, 9, 21, 17, 11.",{"kind":197,"answer":546,"tolerance":199},[],"Largest 21 − smallest 9 = **12**.",[35],{"id":676,"section":35,"level":49,"prompt":677,"check":678,"hints":680,"solution":681,"skills":682},"data-handling.q053","In one day in Jaisalmer the temperature went from a low of 24 °C to a high of 43 °C. What was the range?",{"kind":197,"answer":679,"tolerance":199,"unit":415},19,[],"43 − 24 = **19 °C**. Deserts have big daily ranges because dry air and sand heat up and cool down quickly.",[35],{"id":684,"section":35,"level":109,"prompt":685,"check":686,"hints":688,"solution":690,"skills":691},"data-handling.q054","The range of a set of marks is 35 and the highest mark is 92. What is the lowest mark?",{"kind":197,"answer":687,"tolerance":199},57,[689],"Rearrange: lowest = highest − range.","Range = highest − lowest, so lowest = 92 − 35 = **57**.",[35,692],"inverse",{"id":694,"section":35,"level":109,"prompt":695,"check":696,"hints":707,"solution":708,"skills":709},"data-handling.q055","Two batters each average 40 runs. Batter P's last scores range from 32 to 48; Batter Q's from 0 to 110. Which batter is more consistent?",{"kind":52,"options":697,"correct":706},[698,700,702,704],{"id":55,"label":699},"Batter P",{"id":58,"label":701},"Batter Q",{"id":61,"label":703},"They are equally consistent",{"id":64,"label":705},"You cannot tell without the mode",[55],[],"P's range is 48 − 32 = 16; Q's is 110 − 0 = 110. A smaller range means the scores stay closer together, so **P is more consistent**, even though their means are equal.",[35,710],"comparing",{"id":712,"section":35,"level":109,"prompt":713,"check":714,"hints":715,"solution":717,"skills":718},"data-handling.q056","Every value in a data set is increased by 15. The old range was 23. What is the new range?",{"kind":197,"answer":198,"tolerance":199},[716],"What happens to max − min?","Adding the same amount to every value moves the highest and lowest by 15 each, so their difference is unchanged: **23**.",[35,719],"properties",{"id":721,"section":35,"level":164,"prompt":722,"check":723,"hints":725,"solution":726,"skills":727},"data-handling.q057","Every value in a data set is doubled. The old range was 23. What is the new range?",{"kind":197,"answer":724,"tolerance":199},46,[],"Doubling stretches every gap: the new maximum and minimum are both doubled, so the range doubles to **46**.",[35,719],{"id":729,"section":35,"level":164,"prompt":730,"check":731,"hints":742,"solution":743,"skills":744},"data-handling.q058","A data set is 12, 15, 14, 13, 16, 15, 91. What is the range, and what does it suggest?",{"kind":52,"options":732,"correct":741},[733,735,737,739],{"id":55,"label":734},"79; there is probably an outlier",{"id":58,"label":736},"4; the data is tightly bunched",{"id":61,"label":738},"79; the data is evenly spread",{"id":64,"label":740},"91; the largest value",[55],[],"Range = 91 − 12 = 79. But six of the seven values lie between 12 and 16. The huge range comes from **one outlier, 91**, which should be checked: it might be a typing error for 19. The range is very sensitive to outliers.",[35,745],"outliers",{"id":747,"section":35,"level":281,"prompt":748,"check":749,"hints":751,"solution":753,"skills":754},"data-handling.q059","Five whole numbers have a range of 10, a median of 7 and a mean of 8. The smallest is 3. Find the largest possible value of the second-largest number.",{"kind":197,"answer":750,"tolerance":199},13,[752],"The largest value is 3 + 10 = 13, and d cannot be bigger than it.","Order a ≤ b ≤ c ≤ d ≤ e with a = 3, e = a + 10 = 13, c = 7. Total = 40, so b + d = 40 − 3 − 7 − 13 = 17. To make d as large as possible, make b as small as possible: b ≥ a = 3, so d = 17 − 3 = 14. But d cannot exceed e = 13, so **d = 13** (b = 4). Check: 3, 4, 7, 13, 13 → range 10 ✓, median 7 ✓, mean 40 ÷ 5 = 8 ✓.",[35,23,667],{"id":756,"section":39,"level":49,"prompt":757,"check":758,"hints":765,"solution":766,"skills":767},"data-handling.q060","A shop wants to know which T-shirt size to order the most of. Which average should it use?",{"kind":52,"options":759,"correct":764},[760,761,762,763],{"id":55,"label":24},{"id":58,"label":28},{"id":61,"label":32},{"id":64,"label":36},[61],[],"The shop needs the **most common** size, the mode. A mean size like \"M and a bit\" cannot be bought.",[768],"choosing an average",{"id":770,"section":39,"level":109,"prompt":771,"check":772,"hints":783,"solution":784,"skills":785},"data-handling.q061","Monthly incomes (₹ thousand) in a small office are 18, 20, 22, 22, 25, 28, 30 and 300 (the owner). Which average best describes a typical employee's income?",{"kind":52,"options":773,"correct":782},[774,776,778,780],{"id":55,"label":775},"Mean, about ₹58 thousand",{"id":58,"label":777},"Median, ₹23.5 thousand",{"id":61,"label":779},"Range, ₹282 thousand",{"id":64,"label":781},"The owner's income",[58],[],"Mean = 465 ÷ 8 ≈ 58.1, higher than 7 of the 8 incomes because of the owner's 300. Median = (22 + 25) ÷ 2 = **23.5**, which describes a typical employee. With an outlier, prefer the median.",[768,745],{"id":787,"section":39,"level":109,"prompt":788,"check":789,"hints":791,"solution":792,"skills":793},"data-handling.q062","Weekly pocket money (₹) of six children: 50, 60, 60, 70, 80, 520. By how much is the mean greater than the median?",{"kind":197,"answer":790,"tolerance":199,"unit":405},75,[],"Mean = 840 ÷ 6 = 140. Median = (60 + 70) ÷ 2 = 65. Difference = 140 − 65 = **₹75**. The ₹520 outlier pulls the mean far above the median.",[745,794],"mean vs median",{"id":796,"section":39,"level":109,"prompt":797,"check":798,"hints":803,"solution":804,"skills":805},"data-handling.q063","True or false: \"Adding one very large value to a data set changes the median much more than the mean.\"",{"kind":52,"options":799,"correct":802},[800,801],{"id":97,"label":98},{"id":100,"label":101},[100],[],"False. It is the other way round. A very large value is added to the total, so the **mean** can jump a lot, but it only shifts the middle position of the ordered list by half a place, so the **median** changes little or not at all.",[745],{"id":807,"section":39,"level":109,"prompt":808,"check":809,"hints":820,"solution":821,"skills":822},"data-handling.q064","For which of these would the **mean** be the best average?",{"kind":52,"options":810,"correct":819},[811,813,815,817],{"id":55,"label":812},"Favourite fruit of a class",{"id":58,"label":814},"House prices in a city with a few palaces",{"id":61,"label":816},"Daily rainfall over a month, to estimate the total rain",{"id":64,"label":818},"The most common shoe size",[61],[],"When the **total** matters, the mean is right: total = mean × number of days. Fruit and shoe size need the mode; house prices with palaces need the median.",[768],{"id":824,"section":39,"level":164,"prompt":825,"check":826,"hints":829,"solution":831,"skills":832},"data-handling.q065","A batter scored 10, 45*, 0, 60, 25* in five innings (* = not out). What is the batting average (runs ÷ times out)?",{"kind":197,"answer":827,"tolerance":828},46.67,0.01,[830],"Not-out innings add runs but not dismissals.","Runs = 10 + 45 + 0 + 60 + 25 = 140. Times out = 5 − 2 = 3. Batting average = 140 ÷ 3 ≈ **46.67**. Compare the mean per innings, 140 ÷ 5 = 28: not-outs push the batting average up.",[833],"batting average",{"id":835,"section":39,"level":164,"prompt":836,"check":837,"hints":839,"solution":841,"skills":842},"data-handling.q066","A car goes 60 km at 60 km\u002Fh and then another 60 km at 30 km\u002Fh. What is its average speed for the whole journey?",{"kind":197,"answer":263,"tolerance":199,"unit":838},"km\u002Fh",[840],"Average speed = total distance ÷ total time.","Times: 60 ÷ 60 = 1 h and 60 ÷ 30 = 2 h. Total 120 km in 3 h: 120 ÷ 3 = **40 km\u002Fh**, not (60 + 30) ÷ 2 = 45. The slower part lasted longer, so it counts more.",[478,843],"speed",{"id":845,"section":39,"level":164,"prompt":846,"check":847,"hints":849,"solution":850,"skills":851},"data-handling.q067","Nine people in a room earn ₹30,000 a month each. A person earning ₹30 lakh a month joins them. What is the new **median** monthly income (in ₹)?",{"kind":197,"answer":848,"tolerance":199,"unit":405},30000,[],"In order, the ten incomes are nine 30,000s and one 30,00,000. The median is the mean of the 5th and 6th values, both ₹30,000: **₹30,000**. (The mean jumps to (2,70,000 + 30,00,000) ÷ 10 = ₹3,27,000.)",[745,27],{"id":853,"section":39,"level":281,"prompt":854,"check":855,"hints":866,"solution":867,"skills":868},"data-handling.q068","In a data set, the mean is much larger than the median. Which statement is most likely true?",{"kind":52,"options":856,"correct":865},[857,859,861,863],{"id":55,"label":858},"There are a few unusually large values",{"id":58,"label":860},"There are a few unusually small values",{"id":61,"label":862},"All values are equal",{"id":64,"label":864},"The data is categorical",[55],[],"A few very large values (a long tail on the high side) pull the mean up but barely move the median. This is typical of incomes, rainfall and city populations.",[869,745],"skew",{"id":871,"section":43,"level":49,"prompt":872,"check":873,"hints":874,"solution":876,"skills":877},"data-handling.q069","The mean of 4 numbers is 10. Three of them are 8, 12 and 9. What is the fourth?",{"kind":197,"answer":254,"tolerance":199},[875],"Total = mean × count.","Total = 10 × 4 = 40. 8 + 12 + 9 = 29. Fourth = 40 − 29 = **11**.",[458],{"id":879,"section":43,"level":109,"prompt":880,"check":881,"hints":882,"solution":883,"skills":884},"data-handling.q070","Attendance in a class for 5 days was 38, 40, 35, ? and 37. The mean attendance was 38. How many attended on day 4?",{"kind":197,"answer":263,"tolerance":199},[],"Total = 38 × 5 = 190. Known days: 38 + 40 + 35 + 37 = 150. Day 4 = 190 − 150 = **40**.",[458],{"id":886,"section":43,"level":109,"prompt":887,"check":888,"hints":891,"solution":892,"skills":893},"data-handling.q071","The mean mass of 6 watermelons is 3.5 kg. One watermelon of 5 kg is sold. What is the mean mass of the other 5?",{"kind":197,"answer":889,"tolerance":435,"unit":890},3.2,"kg",[],"Old total = 3.5 × 6 = 21 kg. New total = 21 − 5 = 16 kg. New mean = 16 ÷ 5 = **3.2 kg**.",[458],{"id":895,"section":43,"level":109,"prompt":896,"check":897,"hints":899,"solution":901,"skills":902},"data-handling.q072","A class of 29 students has a mean height of 140 cm. A new student joins and the mean becomes 140.5 cm. How tall is the new student?",{"kind":197,"answer":898,"tolerance":199,"unit":502},155,[900],"Compare the totals before and after.","Old total = 29 × 140 = 4,060 cm. New total = 30 × 140.5 = 4,215 cm. New student = 4,215 − 4,060 = **155 cm**. Another way to see it: the newcomer must bring their own 140.5 plus 0.5 cm for each of the other 29 students: 140.5 + 14.5 = 155.",[458],{"id":904,"section":43,"level":164,"prompt":905,"check":906,"hints":908,"solution":910,"skills":911},"data-handling.q073","The mean of 20 numbers was calculated as 50. It was later found that one number, 68, had been copied as 86. What is the correct mean?",{"kind":197,"answer":907,"tolerance":435},49.1,[909],"Fix the total first.","Wrong total = 50 × 20 = 1,000. It was 86 − 68 = 18 too big. Correct total = 982. Correct mean = 982 ÷ 20 = **49.1**.",[458,912],"errors",{"id":914,"section":43,"level":164,"prompt":915,"check":916,"hints":918,"solution":920,"skills":921},"data-handling.q074","The mean of five consecutive even numbers is 24. What is the largest of them?",{"kind":197,"answer":917,"tolerance":199},28,[919],"The mean of evenly spaced numbers is the middle one.","For evenly spaced numbers the mean is the middle number, 24. The five numbers are 20, 22, 24, 26, 28, so the largest is **28**.",[43],{"id":923,"section":43,"level":164,"prompt":924,"check":925,"hints":926,"solution":927,"skills":928},"data-handling.q075","The mean of 9 numbers is 15. If one number is removed, the mean of the remaining 8 is 14. What number was removed?",{"kind":197,"answer":198,"tolerance":199},[],"Total of 9 = 9 × 15 = 135. Total of 8 = 8 × 14 = 112. Removed number = 135 − 112 = **23**.",[458],{"id":930,"section":43,"level":164,"prompt":931,"check":932,"hints":933,"solution":935,"skills":936},"data-handling.q076","The deviations of 6 values from their mean are −3, 5, −1, 2, −4 and d. What is d?",{"kind":197,"answer":5,"tolerance":199},[934],"Deviations from the mean cancel out.","Deviations from the mean always add up to 0. −3 + 5 − 1 + 2 − 4 = −1, so d = **1**.",[937,43],"deviations",{"id":939,"section":43,"level":281,"prompt":940,"check":941,"hints":942,"solution":944,"skills":945},"data-handling.q077","The mean of 7 numbers is 20. The mean of the first 4 is 18 and the mean of the last 4 is 23. What is the 4th number?",{"kind":197,"answer":292,"tolerance":199},[943],"Which number appears in both groups?","Total of all 7 = 140. First 4 total = 72; last 4 total = 92. Together 72 + 92 = 164, which counts the 4th number twice. So the 4th number = 164 − 140 = **24**.",[946,667],"overlapping groups",{"id":948,"section":43,"level":281,"prompt":949,"check":950,"hints":951,"solution":953,"skills":954},"data-handling.q078","The mean age of a family of 5 is 26 years. Six years ago the youngest child had not been born, and the mean age of the other 4 family members was then 25 years. How old is the youngest child now?",{"kind":197,"answer":236,"tolerance":199},[952],"Everyone who was alive six years ago is now 6 years older.","Now: total age = 5 × 26 = 130. Six years ago the 4 older members had total age 4 × 25 = 100, so today their total is 100 + 4 × 6 = 124. Youngest child = 130 − 124 = **6 years**. (Six years ago the child was just being born, which fits.)",[43,667],{"id":956,"section":43,"level":281,"prompt":957,"check":958,"hints":960,"solution":962,"skills":963},"data-handling.q079","Seven whole numbers have mean 10 and median 12, and all are at least 0. What is the largest possible value of the biggest number?",{"kind":197,"answer":959,"tolerance":199},34,[961],"Numbers after the median cannot be smaller than it.","Order a ≤ … ≤ g with the 4th = 12. The total is 70. Make everything except g as small as allowed: a = b = c = 0, the median 12, and e = f = 12 (they cannot be less than the median). Then g = 70 − (0 + 0 + 0 + 12 + 12 + 12) = **34**.",[667,27,23],{"id":965,"section":43,"level":109,"prompt":966,"check":967,"hints":969,"solution":970,"skills":971},"data-handling.q080","A shopkeeper sold a mean of 45 samosas a day for 6 days. How many samosas must she sell on day 7 so that the 7-day mean is 48?",{"kind":197,"answer":968,"tolerance":199},66,[],"Needed total for 7 days = 48 × 7 = 336. Sold so far = 45 × 6 = 270. Day 7 = 336 − 270 = **66**.",[458],[973,974,975,976,977],"data-handling-ncert-class6-gp","data-handling-ncert-class7","data-handling-ncert-class8","data-handling-khan-summarizing","data-handling-mathsisfun-central","needs_review",{"generatedBy":980,"notes":981},"claude-code","Draft; every numeric answer computed and asserted in Python. Pending owner review.","1e5ba8070a27b826071dc29292f248ba2ccae9f6a0b589ebadb7f7addfed4244",{"logic:questions":984,"source:data-handling-khan-summarizing":985,"source:data-handling-mathsisfun-central":986,"source:data-handling-ncert-class6-gp":987,"source:data-handling-ncert-class7":988,"source:data-handling-ncert-class8":989},"e7fd7c240a65bea1bff6277f7af7cca65e2c7fcb13c6d756cb943d53f3cbc948","d3f02b5bb1750887d4c5e469441199469eba3f40ba38f08a0f15e6dc123789da","0e1e3ad9dc9f84bb51edeb70e657591671f3d8e7326c34f58c2de0c70e823635","3d89b7ad9db743739787967056153b3afc3772805c18a2f4b73fd681b870cc48","73c4938c33c83e313b3e69ea6d4b3fcd121cfeab65eda7e07e1df7901cfaea2c","9c5530663fa1281b78426a548e1488607d718897d812d85bf6a79a1ac289ffb9","preview-7e1cbbcc4f",1789899599571]