NCERT Solutions for Class 7th Maths Chapter 5 Are you a bookworm? — In-text Questions

Book page 107 – 108 Updated on2026-09-19

Q1.

Find the mean and median in Poovizhi's data without the outlier value 118. What change do you notice?

Answer

Without the outlier the mean jumps by more than 10 cm, while the median barely moves.

Remaining heights: 165, 170, 173, 175
Sum = 165 + 170 + 173 + 175 = 683 cm, 4 values
New mean = 683 ÷ 4 = 170.75 cm

Sorted: 165, 170, 173, 175 (even count)
New median = (170 + 173) ÷ 2 = 171.5 cm

	With 118 cm	Without 118 cm	Change
Mean	160.2 cm	170.75 cm	+10.55 cm
Median	170 cm	171.5 cm	+1.5 cm

Why it happens: removing 118 takes a very small number out of the sum, so the mean shoots up. The median only shifts by one position in the sorted list, so it hardly changes. This is the clearest possible demonstration that the median resists outliers and the mean does not.

Tip: notice that the new mean (170.75) and the new median (171.5) are now close together — the sign of data with no outlier left in it.

Q2.

After the summer vacation, a class teacher asked his class how many short stories they had read. Each student answered the number of stories read on a piece of paper, as shown below. Find the mean and median number of short stories read. Before calculating them, can you guess whether the mean will be less than or greater than the median?

The fifteen slips of paper handed in by the class — page 107.

Answer

The guess: the mean will be greater than the median. One student read 40 stories while everybody else read 15 or fewer — a high outlier drags the mean up but leaves the median where it is.

Now the calculation. There are 15 papers: 6, 8, 5, 15, 40, 0, 8, 3, 0, 2, 7, 12, 5, 1, 10.

Sum = 6 + 8 + 5 + 15 + 40 + 0 + 8 + 3 + 0 + 2 + 7 + 12 + 5 + 1 + 10
= 14 + 5 + 15 + 40 + 0 + 8 + 3 + 0 + 2 + 7 + 12 + 5 + 1 + 10
= 122
Mean = 122 ÷ 15 ≈ 8.13 stories

Sorted: 0, 0, 1, 2, 3, 5, 5, 6, 7, 8, 8, 10, 12, 15, 40
15 values, so the middle one is the 8th → Median = 6 stories

Why it happens: the mean 8.13 is bigger than 11 of the 15 values. The single reading of 40 adds 40 to the sum all by itself — a third of the entire total came from one student. The median simply counts positions, so that one student is just "the last one in the line" and moves nothing.

Check it yourself: the book states that the median is 6 and that half the class read 6 or more stories. Count them: 6, 7, 8, 8, 10, 12, 15, 40 — that is 8 students at or above 6, out of 15. Correct.

Q3.

Mark the data, the mean, and the median on the dot plot below.

Page 108 — the empty dot plot printed with this question, with its scale running from 0 to 25.

Answer

The number line runs from 0 to 40. Place one dot for each value, stacking repeats. Then draw a solid line at the mean 8.13 and a dashed line at the median 6.

Value	0	1	2	3	5	6	7	8	10	12	15	40
Number of dots	2	1	1	1	2	1	1	2	1	1	1	1

Dot plot of the number of short stories read. The dots crowd between 0 and 15; the lone dot at 40 is the outlier, and it pulls the mean (solid line) to the right of the median (dashed line).

Why it happens: the picture shows in one glance what the two numbers only hint at — fourteen dots huddle in the first quarter of the line and one sits far away at the end. That gap is the outlier.

Q4.

Which of the values would you consider an outlier?

Answer

40 is the outlier.

All the other values: 0, 0, 1, 2, 3, 5, 5, 6, 7, 8, 8, 10, 12, 15
Next highest value after 40 is 15
Gap between them = 40 − 15 = 25 stories
Gap between any other neighbouring pair ≤ 3

Why it happens: an outlier is a value that significantly deviates from the rest. Here the whole class sits inside a band of 15 stories, and then there is an empty stretch of 25 before the single reading of 40. That empty stretch is the evidence.

Careful: 15 is the second highest value, but it is not an outlier — it is only 3 above 12, which is only 2 above 10. The values step up smoothly until 40.

Q5.

Find the mean and median in the absence of the outlier. What change do you notice?

Answer

Removing 40 pulls the mean down by more than 2 stories; the median drops by only half a story.

New sum = 122 − 40 = 82, and 14 values remain
New mean = 82 ÷ 14 ≈ 5.86 stories

Sorted: 0, 0, 1, 2, 3, 5, 5, 6, 7, 8, 8, 10, 12, 15
Even count, so New median = (5 + 6) ÷ 2 = 5.5 stories

	With 40	Without 40	Change
Mean	8.13	5.86	−2.27
Median	6	5.5	−0.5

Why it happens: the mean changed more than four times as much as the median. Notice also that mean and median have now swapped places — before removal mean > median (8.13 > 6); afterwards they are almost equal (5.86 and 5.5). Once the high outlier is gone, the data is balanced again.

The rule: a very high outlier lifts the mean, so mean > median. A very low outlier (like 118 cm in Poovizhi's family) drops the mean, so mean < median.

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