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NCERT Solutions for Class 7th Maths Chapter 5 Of Ends and the Essence — In-text Questions

Book page 109 – 110 Updated on2026-09-19

Q1.
Suppose you are asked the question, “How tall is your class?” What would you say? [Boys: 147, 135, 130, 154, 128, 135, 134, 158, 155, 146, 146, 142, 140, 141, 144, 145, 150. Girls: 143, 136, 150, 144, 154, 140, 145, 148, 156, 150, 150.]
Answer

No single number answers this well. A good answer gives a typical height and the two ends.

Boys (17 values): sum = 2430, mean = 2430 ÷ 17 ≈ 142.94 cm
Boys sorted: 128, 130, 134, 135, 135, 140, 141, 142, 144, 145, 146, 146, 147, 150, 154, 155, 158
Median = 9th value = 144 cm

Girls (11 values): sum = 1616, mean = 1616 ÷ 11 ≈ 146.9 cm
Girls sorted: 136, 140, 143, 144, 145, 148, 150, 150, 150, 154, 156
Median = 6th value = 148 cm

Whole class (28 students): sum = 2430 + 1616 = 4046
Mean = 4046 ÷ 28 = 144.5 cm   Median = 145 cm

So a full answer is: the class is about 145 cm tall on average, with everybody between 128 cm and 158 cm.

Why it happens: "How tall is your class?" is a statistical question — the answer varies from student to student. Giving only the mean hides the 30 cm spread between the shortest and the tallest. Giving the mean, the median and the two ends describes the class honestly.
Note on the book's figure: the printed dot plot gives the whole-class mean as 144.4 cm. Adding the 28 heights gives 4046, and 4046 ÷ 28 = 144.5 exactly. The correct mean is 144.5 cm. Nothing else in the discussion changes.
Q2.
What can we infer from the dot plots and the central tendency measures?
Answer

Four things can be said, and the book states them all.

Boys (17)Girls (11)Whole class (28)
Shortest128 cm136 cm128 cm
Tallest158 cm156 cm158 cm
Range30 cm20 cm30 cm
Mean142.94 cm146.9 cm144.5 cm
Median144 cm148 cm145 cm
  • The boys' heights are more spread out, from 128 to 158 cm. The girls lie in a narrower band, 136 to 156 cm.
  • Both the tallest and the shortest student in the class are boys.
  • Yet the boys' mean is below the class mean and below the girls' mean. In this class the girls are taller on average.
  • For both groups mean < median (142.94 < 144 and 146.9 < 148), which shows a small pull from values on the lower side.
Why it happens: the boys' group contains the extremes at both ends, but it also has more students bunched in the 128–142 range. Extremes decide the range; the bulk of the values decides the mean.
Say it carefully: "the girls are taller than the boys in this class" is a statement about the averages. It certainly does not mean every girl is taller than every boy — the tallest person in the class is a boy at 158 cm.
Q3.
How many students are taller than the class' average height?
Answer

15 students out of 28 are taller than the class average of 144.5 cm.

All 28 heights sorted:
128, 130, 134, 135, 135, 136, 140, 140, 141, 142, 143, 144, 144,
145, 145, 146, 146, 147, 148, 150, 150, 150, 150, 154, 154, 155, 156, 158

Class mean = 144.5 cm
Heights above 144.5: 145, 145, 146, 146, 147, 148, 150, 150, 150, 150, 154, 154, 155, 156, 158
Count = 15 students
Why it happens: 15 out of 28 is a little over half. That is quite normal — the mean does not have to split a group into two equal halves. Only the median does that. Here the median is 145 cm, and 13 students are below it, 13 above, with 2 students at exactly 145.
Tip: using the book's printed mean of 144.4 cm gives the same count of 15, because no student is exactly 144.4 or 144.5 cm tall.
Q4.
How many boys are taller than the class' average height?
Answer

8 boys are taller than 144.5 cm.

Boys sorted: 128, 130, 134, 135, 135, 140, 141, 142, 144,
145, 146, 146, 147, 150, 154, 155, 158

Boys above 144.5 cm: 145, 146, 146, 147, 150, 154, 155, 158 → 8 boys
Boys at or below 144.5 cm: 17 − 8 = 9 boys
Why it happens: only 8 of the 17 boys (less than half) reach the class average, while 7 of the 11 girls do (145, 148, 150, 150, 150, 154, 156). That is another way of seeing the same fact — the girls in this class are on the whole taller.
Check it yourself: 8 boys + 7 girls = 15 students above the class average. That matches the previous answer exactly.
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