NCERT Solutions for Class 7th Maths Chapter 5 Measures of Central Tendency — Math Talk

Book page 108 – 109 Updated on2026-09-19

Q1.

In the three examples we considered — the heights, short-stories, and newspaper pages — observe the variability in data when: (a) the mean and median are close to each other (b) the mean and median are comparatively far apart, with mean < median (c) the mean and median are comparatively far apart, with mean > median

Answer

Each of the three examples illustrates exactly one of the three cases.

Case	Example	Mean	Median	What the data looks like
(a) close together	Newspaper pages 10, 16, 16, 18, 20, 22, 26	18.29	18	Values spread out evenly, no value far from the rest
(b) mean < median	Poovizhi's family 118, 165, 170, 173, 175	160.2	170	One value far below the rest — a low outlier
(c) mean > median	Short stories 0, 0, 1, 2, 3, 5, 5, 6, 7, 8, 8, 10, 12, 15, 40	8.13	6	One value far above the rest — a high outlier

Why it happens: the median is anchored to the middle position and cannot be dragged. The mean is a balance point, so it slides towards whichever side the extreme value is on. A low value drags it down and it falls below the median; a high value drags it up and it rises above the median. When nothing extreme exists, there is nothing to drag it and the two sit together.

Tip: you can use this backwards. If you are told only that a set of exam marks has mean 42 and median 55, you already know that a few very low marks are pulling the mean down — without seeing a single mark.

Q2.

Discuss the effect on the mean and median when outliers are present on both sides. You may take some example data to examine and explain this.

Answer

When there is a low outlier and a high outlier, the two pulls act in opposite directions. Whether the mean ends up above or below the median depends on which outlier is further from the middle.

Case 1 — the two outliers balance. Take 2, 18, 19, 20, 21, 22, 38.

Sum = 2 + 18 + 19 + 20 + 21 + 22 + 38 = 140
Mean = 140 ÷ 7 = 20 Median = 4th value = 20
2 is 18 below the middle; 38 is 18 above it — the pulls cancel

Case 2 — the high outlier is further away. Take 2, 18, 19, 20, 21, 22, 60.

Sum = 162, Mean = 162 ÷ 7 ≈ 23.14 Median = 20
Mean > median, because 60 is 40 above the middle while 2 is only 18 below

Case 3 — the low outlier is further away. Take 0, 18, 19, 20, 21, 22, 26.

Sum = 126, Mean = 126 ÷ 7 = 18 Median = 20
Mean < median, because 0 is 20 below the middle while 26 is only 6 above

Why it happens: the mean adds up distances, so it responds to how far each outlier is, not just to how many there are. The median counts positions, so both outliers are simply "first in the line" and "last in the line" — and removing or moving them further out changes the median not at all.

The warning to carry away: in Case 1 the mean and median are equal, which normally suggests balanced data — but the data is not balanced, it has two wild values that happen to cancel. So mean = median is good evidence of balance, not proof of it. Always look at the dot plot as well.

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