NCERT Solutions for Class 7th Maths Chapter 5 Math Talk — Representative Values

Book page 98 – 99 Updated on2026-09-19

Q1.

The runs scored by Shubman and Yashasvi in a cricket series are given in the table below. Who do you think performed better?

	Match 1	Match 2	Match 3	Match 4
Shubman	0	17	21	90
Yashasvi	67	55	18	35

Runs scored by the two players in the first series — page 98.

Answer

Yashasvi performed better in this series, but the honest answer is that it depends on what you count — and the children in the book each count something different.

Way of comparing	Shubman	Yashasvi	Better
Highest score	90	67	Shubman
Total runs	0+17+21+90 = 128	67+55+18+35 = 175	Yashasvi
Mean per match	128 ÷ 4 = 32	175 ÷ 4 = 43.75	Yashasvi
Range (max − min)	90 − 0 = 90	67 − 18 = 49	Yashasvi (steadier)
Matches won head-to-head	Matches 3, 4	Matches 1, 2	Equal

Why it happens: both played the same number of matches, so the total is a fair comparison here, and Yashasvi's total is larger. He is also more consistent — his scores stay between 18 and 67, while Shubman swings from 0 to 90. Vaishnavi is right that Shubman hit the single biggest score, but one big innings does not make a whole series.

Tip: Shreyas's first remark — "Yashasvi scored more in the first two, Shubman in the last two, so they are similar" — only counts how many times each was ahead. It ignores by how much. Shubman's win in Match 4 was by 55 runs; Yashasvi's win in Match 2 was by 38. Counting wins throws that away.

Q2.

The table below shows the runs scored by these two players in another series. Who do you think performed better in this series?

	Match 1	Match 2	Match 3	Match 4	Match 5
Shubman	23	07	10	52	18
Yashasvi	26	53	02	-	15

Runs scored by the two players in the second series — page 99.

Answer

Yashasvi performed better — he averaged more runs per match, even though Shubman's total is larger.

Shubman: 23 + 7 + 10 + 52 + 18 = 110 runs in 5 matches
Yashasvi: 26 + 53 + 2 + 15 = 96 runs in 4 matches (he did not play Match 4)
Mean for Shubman = 110 ÷ 5 = 22 runs per match
Mean for Yashasvi = 96 ÷ 4 = 24 runs per match

Why it happens: the two players did not play the same number of matches, so the total is no longer a fair measure. Shubman had one extra chance to add runs. Dividing by the number of matches played puts both on the same footing — that is exactly what the mean does.

Check it yourself: if Shubman had played only 4 matches and scored his best four (23, 10, 52, 18 = 103), his mean would have been 25.75. The comparison really does depend on how many matches each played.

Q3.

Vaishnavi says, “Here, Shubman performed better since his total is 110 runs, while Yashasvi's total is 96 runs”. What do you think of Vaishnavi's statement?

Answer

Her arithmetic is right, but her conclusion is not safe. The two totals are not comparable, because they come from different numbers of matches.

110 runs from 5 matches → 110 ÷ 5 = 22 per match
96 runs from 4 matches → 96 ÷ 4 = 24 per match

Why it happens: a total grows simply by playing more. Shreyas spots this at once — "But Yashasvi made 96 runs in 4 matches and Shubman made 110 in 5." Whenever two groups are of different sizes, compare a per-item value (the mean), not the raw total.

Tip: the same trap appears everywhere. A shop that sold ₹50,000 of goods in 10 days did not do better than one that sold ₹30,000 in 5 days — that is ₹5,000 a day against ₹6,000 a day.

Q4.

Can a single number act as a representative of a group of numbers? For example, can we represent Shubman's or Yashasvi's batting in this series with one number? Discuss.

Answer

Yes — one number can represent a group, but it can never replace it.

The total is one such number, and it works when the groups are the same size.
The mean (average) works even when the groups differ in size, because it balances the highs and the lows: Shubman 22, Yashasvi 24.
The highest score and the range are also single numbers, but each tells only one thing.

Why it happens: the mean is a levelling value. If Shubman had scored 22 in every one of his five matches, his total would still be 110. So 22 is the score that, repeated, gives the same total — it stands in for the whole group.

But be careful: a single number hides everything else. Shubman's mean of 22 does not tell you that one of his scores was 52 and another was 7. That is why we also look at the minimum, the maximum and the spread.

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