"Mathematics — Data Handling" — Practice

Question 1

Find the mean of the following marks scored by 5 students: 10, 12, 14, 20, 34.
(a) 18  (b) 14  (c) 34  (d) 90

Accepted Answer

Sum = 10+12+14+20+34 = 90. Mean = 90/5 = 18.

Answer: (a) 18. Trap (b) 14 is the median of this same dataset (the middle sorted value: 10,12,14,20,34), mistakenly reported instead of the mean — exactly the mean/median mix-up this chapter warns about. Trap (c) 34 is simply the largest value in the dataset, mistaken for a 'representative' figure instead of actually computing the mean. Trap (d) 90 is the correct sum, but stops there and forgets the final step of dividing by the number of observations (5).

Question 2

Shoe sizes sold in a day at a shop: 6, 7, 6, 8, 6, 9, 7. Find the mode.
(a) 6  (b) 7  (c) 8  (d) No mode

Accepted Answer

Size 6 occurs three times (more than any other size: 7 occurs twice, 8 and 9 once each). Mode = 6.

Answer: (a) 6. Trap (b) 7 is both the mean and the median of this dataset (sum=49, mean=7; sorted 6,6,6,7,7,8,9, median=4th term=7) — easy to confuse with the mode since it's a different measure entirely ('most frequent' versus 'average'/'middle'). Trap (c) 8 appears only once in the data and is easy to wrongly flag as the mode if the tally count is rushed. Trap (d) 'No mode' wrongly assumes every value occurs equally often, overlooking that 6 clearly repeats three times.

Question 3

Find the median of the following weekly pocket-money amounts (in rupees) of 6 students: 22, 95, 14, 61, 38, 8.
(a) 30  (b) 22  (c) 38  (d) 49.5

Accepted Answer

Sort first: 8, 14, 22, 38, 61, 95. With n=6 (even), the median is the average of the 3rd and 4th terms: (22+38)/2 = 30.

Answer: (a) 30. Trap (b) 22 picks only the 3rd term (the lower of the two true middle terms) and stops there, instead of averaging both middle terms as an even-sized dataset requires. Trap (c) 38 is the mirror error, picking only the 4th (higher) middle term alone. Trap (d) 49.5 is an off-by-one positioning slip — averaging the 4th and 5th terms (38 and 61) instead of correctly identifying the 3rd and 4th terms as the true middle pair for n=6.

Question 4

In a bar graph, the vertical axis is marked in gridlines where each gridline represents 5 students. The bar for 'Cricket' reaches exactly the 4th gridline. How many students chose cricket?
(a) 20  (b) 4  (c) 24  (d) 16

Accepted Answer

Value = gridline position x scale per gridline = 4 x 5 = 20 students.

Answer: (a) 20. Trap (b) 4 reads the raw gridline count directly as the answer, ignoring that each gridline actually represents 5 units, not 1 — the classic scale-misreading error this chapter is built to catch. Trap (c) 24 misremembers the scale as 6 units per gridline instead of the stated 5, computing 4x6 instead of 4x5. Trap (d) 16 confuses the bar's gridline position (4) with the scale value itself and multiplies 4x4, instead of correctly multiplying the gridline count by the stated scale of 5.

Question 5

A pictograph of fruit sold uses the key: one apple symbol = 6 kg. Monday's row shows 2 full symbols and 1 half symbol. How many kilograms were sold on Monday?
(a) 15  (b) 12  (c) 18  (d) 13

Accepted Answer

Value = (2 full symbols x 6 kg) + (half symbol x 3 kg) = 12 + 3 = 15 kg.

Answer: (a) 15. Trap (b) 12 counts only the two full symbols and ignores the half-symbol entirely. Trap (c) 18 treats the half-symbol as a full symbol, giving 3x6=18 instead of correctly counting it as half a symbol's value. Trap (d) 13 treats the half-symbol as contributing a flat '1' unit rather than half the key's actual value (12+1=13), instead of correctly adding half of 6 (=3).

Question 6

Which of the following is NOT a genuine distinguishing feature between a histogram and an ordinary bar graph representing categorical data?
(a) A histogram has no gaps between adjacent bars
(b) A histogram represents continuous class-interval data
(c) A histogram's bars must all be drawn in the same colour
(d) A histogram's bar width corresponds to the class size

Accepted Answer

Options (a), (b) and (d) are all real, testable differences between a histogram and a bar graph. Bar colour, however, is purely a presentation choice available to either chart type and has nothing to do with what actually makes a histogram different — making (c) the correct answer to a 'which is NOT true' question.

Answer: (c). Trap (a) is a real, defining feature (no gaps, because the class intervals are continuous and share boundaries) — a wrong pick here mistakes a true statement for the false one being asked for. Trap (b) is also genuinely true — continuous grouped data is exactly what a histogram represents, unlike a bar graph's discrete categories. Trap (d) is true as well — bar width tied to class size is a real structural feature of histograms; none of (a), (b) or (d) is the 'odd one out' the question is looking for.

Question 7

A pie chart shows sports preferences among 450 students in total. The 'Football' sector has a central angle of 60°. How many students preferred football?
(a) 75  (b) 60  (c) 90  (d) 120

Accepted Answer

Value = (sector angle / 360°) x total = (60/360) x 450 = (1/6) x 450 = 75.

Answer: (a) 75. Trap (b) 60 mistakes the angle itself (60°) for the number of students, without applying the sector formula at all. Trap (c) 90 uses an incorrect denominator (such as 300° instead of the full 360° circle) as the base of the ratio. Trap (d) 120 misreads the sector's angle as 120° instead of the stated 60° — perhaps confusing it with a neighbouring sector — and then applies the formula correctly to the wrong angle value.

Question 8

A coin is tossed 25 times and lands on tails 15 times. What is the experimental probability of getting heads?
(a) 2/5  (b) 3/5  (c) 1/2  (d) 10/15

Accepted Answer

Heads occurred on 25−15 = 10 tosses. P(heads) = 10/25 = 2/5.

Answer: (a) 2/5. Trap (b) 3/5 is actually the probability of TAILS (15/25), mistakenly reported instead of the probability of heads that the question asked for. Trap (c) 1/2 assumes the coin is 'fair' and reports the theoretical probability instead of using the actual recorded trial data — exactly the theoretical-vs-empirical confusion this chapter tests. Trap (d) 10/15 divides the number of heads by the number of tails instead of by the total number of trials, an incorrect ratio construction.

Question 9

Before formally teaching bar graphs, a Class VI teacher asks each student to state their favourite fruit, tallies the responses on the board as a class activity, and only then teaches how to convert that tally into a bar graph. This approach best reflects which NCERT-recommended principle for teaching Data Handling?
(a) Beginning with abstract, textbook-supplied datasets to save classroom time
(b) Starting with real, learner-generated data before teaching the formal representation
(c) Testing students on graph formulas before any data collection occurs
(d) Avoiding classroom data-collection activities since they are not part of the syllabus

Accepted Answer

Collecting data the children themselves generate (their own favourite fruit, in this case) before teaching the formal graph-building technique on top of it is exactly the NCERT-recommended entry point for Data Handling described in this chapter.

Answer: (b). Trap (a) describes the opposite of NCERT's recommended approach — starting from an abstract, externally supplied dataset rather than data the children generated themselves. Trap (c) reverses the intended sequence entirely: NCERT recommends collecting and engaging with real data BEFORE introducing the formal representation or calculation, not testing formulas first. Trap (d) is factually wrong on two counts — hands-on data collection is explicitly recommended, not merely tolerated, and it sits squarely within the intended pedagogical approach for this chapter, not outside the syllabus.

Practice — "Mathematics — Data Handling"

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