NCERT Solutions for Class 7th Maths Chapter 5 Telling Tall Tales — Math Talk

Book page 127 – 128 Updated on2026-09-19

Q1.

Spend sufficient time observing the data presented in this table. Share your findings with the class. These are some prompts for you to probe — Changes in the heights of boys or girls of a certain age from 1989 to 2019. The heights of boys vs. girls at different ages in a particular year. Changes in height between successive ages in boys and girls in 2019.

Age	1989		1999		2009		2019
Age	Boys	Girls	Boys	Girls	Boys	Girls	Boys	Girls
5	101.3	100	102.4	101.7	105.1	104	107.1	107.2
6	107.5	106	108.7	107.5	111	109.7	113.1	112.9
7	113	111.4	114.2	112.6	116.2	114.8	118.6	118
8	118.1	116.5	119.2	117.5	120.9	119.6	123.5	122.7
9	122.9	121.7	123.9	122.4	125.2	124.5	128.1	127.6
10	127.5	127.3	128.3	127.8	129.4	129.9	132.6	132.8
11	132.2	133.4	132.8	133.6	133.7	135.7	137	138.6
12	137.7	139	138	139.1	138.9	141.1	142.2	143.8
13	144.2	143.2	144.3	143.1	145.2	145.1	148.4	147.7
14	150.6	146.2	150.5	146.1	151.5	148	154.4	150.4
15	155.4	148.5	155.2	148.4	156.3	150.1	159	152.4
16	158.9	150.1	158.7	150.1	159.9	151.6	162.3	153.8
17	161.3	151.2	161.4	151.3	162.6	152.6	164.6	154.7
18	162.9	151.8	163.2	152.1	164.3	153	166	155.2
19	163.5	151.9	164.2	152.4	165.1	153	166.5	155.2

Average heights, in cm, of boys and girls at each age in 1989, 1999, 2009 and 2019 — page 127.

Answer

Take the three prompts one at a time.

1. Change from 1989 to 2019 at a fixed age. Read across a row.

Age	Boys 1989	Boys 2019	Gain	Girls 1989	Girls 2019	Gain
5	101.3	107.1	+5.8	100.0	107.2	+7.2
10	127.5	132.6	+5.1	127.3	132.8	+5.5
15	155.4	159.0	+3.6	148.5	152.4	+3.9
19	163.5	166.5	+3.0	151.9	155.2	+3.3

Indians of every age got taller over these 30 years. The gain is largest for the youngest children (about 6–7 cm at age 5) and smallest at 19 (about 3 cm). Girls gained slightly more than boys at every age shown.

2. Boys against girls in one year. Read a pair of columns down.

Ages 5 to 9: boys are a little taller — by 1 cm or less. (The one exception is age 5 in 2019, where girls edge ahead by 0.1 cm.)
Ages 10 to 12: the order reverses. In 2019, 11-year-old girls average 138.6 cm against boys' 137.0 cm, and 12-year-old girls 143.8 cm against boys' 142.2 cm. Girls have their growth spurt earlier.
Age 13 onwards: boys pull ahead and stay ahead. By 19 the gap is 166.5 − 155.2 = 11.3 cm.

3. Growth between successive ages in 2019.

From age → to age	5→6	9→10	10→11	12→13	13→14	15→16	17→18	18→19
Boys grow (cm)	6.0	4.5	4.4	6.2	6.0	3.3	1.4	0.5
Girls grow (cm)	5.7	5.2	5.8	3.9	2.7	1.4	0.5	0.0

Both grow fast at 5, slow down in the middle years, then speed up again for the growth spurt — girls at about 10 to 11, boys at about 12 to 13. After the spurt both slow sharply, and by 18–19 girls have practically stopped.

Why boys end up taller: not because they grow faster, but because they grow for longer. Girls' spurt comes about two years earlier and finishes earlier, so boys keep adding a few centimetres a year at ages when girls have stopped.

Q2.

Which of the following statements can be justified using the data? 1. The average heights of both boys and girls at every age increased from 1989 to 2019. 2. The average height of 13-year-old girls in 1989 is more than the average height of 14-year-old girls in 2009. 3. The average height of 15-year-old boys in 2019 is more than the average height of 16-year-old boys in 1989. 4. All girls aged 13 are taller than all girls aged 11. 5. Throughout the age period 5 to 19, the average boy's height is more than the average girl's height. 6. Boys keep growing even beyond age 19.

Answer

Statement	Justified?	The evidence
1. Every age increased, 1989 → 2019	Yes	Compare the 1989 and 2019 columns row by row. Every one of the 15 ages is higher in 2019, for boys and for girls.
2. 13-year-old girls in 1989 > 14-year-old girls in 2009	No	1989, age 13 girls = 143.2 cm. 2009, age 14 girls = 148.0 cm. So 143.2 < 148.0 — the statement is the wrong way round.
3. 15-year-old boys in 2019 > 16-year-old boys in 1989	Yes	2019, age 15 boys = 159.0 cm. 1989, age 16 boys = 158.9 cm. True — but by only 0.1 cm.
4. All girls aged 13 are taller than all girls aged 11	No	The table gives averages only. It contains nothing at all about individual girls, so it can neither prove nor disprove a claim about every girl.
5. Boys taller than girls throughout ages 5 to 19	No	At ages 11 and 12, girls are taller in all four years. In 2019, age 11: girls 138.6 vs boys 137.0; age 12: girls 143.8 vs boys 142.2. Girls are also taller at age 10 in 2009 and 2019.
6. Boys keep growing beyond age 19	No	The table stops at 19, so it holds no evidence either way. What it does show is that growth is nearly over: boys gain only 0.5 cm from 18 to 19 in 2019.

Statement 1 needs one careful note: it is true when you compare the two end years, 1989 and 2019 — all 15 ages rose, for boys and for girls. It would be false if you read it as "increased at every ten-year step", because several ages dipped slightly between 1989 and 1999: 13-year-old girls fell from 143.2 cm to 143.1 cm, 14-year-old boys from 150.6 cm to 150.5 cm, and the same happened at ages 15 and 16. The safe answer is: justified as a comparison of 1989 with 2019, not as a claim about every ten-year step.

Three different reasons for saying "No": statement 2 is disproved by the numbers. Statement 5 is disproved too. Statements 4 and 6 are unsupported — the table simply does not contain that kind of information. Keeping "false" apart from "not shown" is what makes an answer honest.

Q3.

In 2019, between which two successive ages from 5 to 19 did boys grow the most? Between which two successive ages from 5 to 19 did girls grow most?

Answer

Boys grew most between ages 12 and 13 (+6.2 cm). Girls grew most between ages 10 and 11 (+5.8 cm).

Boys 2019, biggest steps:
12 → 13: 148.4 − 142.2 = 6.2 cm (largest)
5 → 6: 113.1 − 107.1 = 6.0 cm
13 → 14: 154.4 − 148.4 = 6.0 cm

Girls 2019, biggest steps:
10 → 11: 138.6 − 132.8 = 5.8 cm (largest)
5 → 6: 112.9 − 107.2 = 5.7 cm
9 → 10: 132.8 − 127.6 = 5.2 cm
11 → 12: 143.8 − 138.6 = 5.2 cm

Why it happens: these two peaks are the growth spurt, and the girls' comes about two years earlier than the boys'. That is exactly why girls are taller than boys at ages 10, 11 and 12 — they have already begun their spurt while the boys are still in their slow years, growing about 4.4 cm a year.

Careful: for boys the top three steps are 6.2, 6.0 and 6.0 cm — very close together. Heights in the table are rounded to one decimal place, so a difference of 0.2 cm is at the edge of what the data can really tell us. The safest answer is that boys grow fastest somewhere between ages 12 and 14.

Q4.

Suppose the average height of a newborn is 50 cm. Estimate the average height of young children of ages 1 to 4.

Answer

The table starts at age 5, where a child averages about 107 cm (2019). So a child grows about 57 cm in its first five years.

A first estimate — share the growth equally.

Total growth from birth to age 5 = 107 − 50 = 57 cm
If it were spread evenly: 57 ÷ 5 = 11.4 cm each year
Age 1 ≈ 61 cm, age 2 ≈ 73 cm, age 3 ≈ 84 cm, age 4 ≈ 96 cm

A better estimate — growth slows down with age. The table itself shows this: children gain about 6 cm a year at age 5, but only 0.5 cm a year at age 18. Running that pattern backwards, the first year should be by far the biggest. So give the early years more than 11.4 cm and the later years less.

Age	Birth	1	2	3	4	5
Even-share estimate	50	61	73	84	96	107
Slowing-growth estimate	50	≈ 75	≈ 87	≈ 95	≈ 101	107
Growth that year (cm)	—	25	12	8	6	6

Why the second estimate is better: the even-share figure of 11.4 cm a year would mean a one-year-old grows no faster than a five-year-old. But the table's own trend — bigger gains at younger ages — says the opposite. A baby grows about half its birth length in its first year, and then the rate falls away steeply.

Be honest about it: both are estimates, not readings. The table contains no data at all for ages 0 to 4, so the right way to report this is "somewhere around 75 cm at age 1", not "75 cm at age 1".

Q5.

Based on the trend observed in the table, write your estimates of the heights of boys and girls for ages 5 to 19 in the year 2029.

Age	1989		1999		2009		2019
Age	Boys	Girls	Boys	Girls	Boys	Girls	Boys	Girls
5	101.3	100	102.4	101.7	105.1	104	107.1	107.2
6	107.5	106	108.7	107.5	111	109.7	113.1	112.9
7	113	111.4	114.2	112.6	116.2	114.8	118.6	118
8	118.1	116.5	119.2	117.5	120.9	119.6	123.5	122.7
9	122.9	121.7	123.9	122.4	125.2	124.5	128.1	127.6
10	127.5	127.3	128.3	127.8	129.4	129.9	132.6	132.8
11	132.2	133.4	132.8	133.6	133.7	135.7	137	138.6
12	137.7	139	138	139.1	138.9	141.1	142.2	143.8
13	144.2	143.2	144.3	143.1	145.2	145.1	148.4	147.7
14	150.6	146.2	150.5	146.1	151.5	148	154.4	150.4
15	155.4	148.5	155.2	148.4	156.3	150.1	159	152.4
16	158.9	150.1	158.7	150.1	159.9	151.6	162.3	153.8
17	161.3	151.2	161.4	151.3	162.6	152.6	164.6	154.7
18	162.9	151.8	163.2	152.1	164.3	153	166	155.2
19	163.5	151.9	164.2	152.4	165.1	153	166.5	155.2

Average heights, in cm, of boys and girls at each age in 1989, 1999, 2009 and 2019 — page 127.

Answer

Look first at how much each age gained in the most recent ten years, 2009 → 2019, and then add a similar amount again.

Age	Boys 2009	Boys 2019	Gain	Estimate 2029
5	105.1	107.1	+2.0	≈ 109
8	120.9	123.5	+2.6	≈ 126
11	133.7	137.0	+3.3	≈ 140
14	151.5	154.4	+2.9	≈ 157
17	162.6	164.6	+2.0	≈ 167
19	165.1	166.5	+1.4	≈ 168

Age	Girls 2009	Girls 2019	Gain	Estimate 2029
5	104.0	107.2	+3.2	≈ 110
8	119.6	122.7	+3.1	≈ 126
11	135.7	138.6	+2.9	≈ 141
14	148.0	150.4	+2.4	≈ 153
17	152.6	154.7	+2.1	≈ 157
19	153.0	155.2	+2.2	≈ 157

The rule of thumb: add about 2 to 3 cm to each 2019 value — a little more at the younger ages, a little less at 18 and 19.

Why this is only an estimate: we are assuming the next ten years behave like the last ten. That is a reasonable assumption, but it is an assumption. The gains have in fact been getting smaller over the three decades (about +2 cm from 1989 to 1999, about +2 cm from 1999 to 2009, then about +2.5 cm from 2009 to 2019), and growth in average height cannot go on for ever.

How to state a prediction properly: say "if the trend of the last thirty years continues, a 19-year-old boy in 2029 would average about 168 cm." The condition at the front is part of the answer, not decoration.

Q6.

How is the graph organised? What information is presented?

Average heights of 19-year-old boys and girls in 28 countries in 1989 and 2019 — page 128. Values read off the printed graph.

Answer

How it is organised. Along the bottom are countries — Timor-Leste, Yemen, Bangladesh, Liberia, Indonesia, India, Bhutan, Pakistan, Maldives, Kenya, Saudi Arabia, Japan, Sudan, Taiwan, Italy, Egypt, South Korea, China, Israel, Turkey, Libya, New Zealand, U.K., Australia, Norway, Ukraine, Iceland, Netherlands. They are arranged from the shortest on the left to the tallest on the right.

What is plotted. For each country there are four marks, not bars:

Mark	Meaning
Orange ×	Boys in 1989 (B-1989)
Blue ×	Boys in 2019 (B-2019)
Orange ▲	Girls in 1989 (G-1989)
Blue ▲	Girls in 2019 (G-2019)

So the shape of a mark says boy or girl, and its colour says 1989 or 2019. Everyone shown is 19 years old.

The scale. The vertical line is labelled 145, 155, 165, 175, 185 cm — it starts at 145 cm, not at 0. This zooms in so that a difference of 2 or 3 cm is visible. Without the zoom, all the marks would be squeezed into the top sliver of the graph and no difference could be seen at all.

Why cutting the axis is fair here: nobody is anywhere near 0 cm tall, so the space between 0 and 145 would carry no information. The graph is honest because it labels where the axis starts. The danger is only when a cut axis is not labelled — then a tiny difference can be made to look enormous.

Q7.

What do you find interesting?

Answer

Five things stand out.

The range between countries is enormous. The tallest 19-year-old boys, in the Netherlands, average about 183 cm; in Timor-Leste about 160 cm — a gap of more than 20 cm, far bigger than any change over 30 years within one country.
Boys are taller than girls in every single country shown. The × marks sit above the ▲ marks all the way across, and the gap is roughly 10–13 cm everywhere.
Almost every country got taller between 1989 and 2019 — the blue marks generally sit above the orange ones for both boys and girls.
The growth was not equal. South Korea and China rose steeply over the 30 years, while some already-tall countries such as the Netherlands barely moved. Countries that started shorter often gained the most.
India sits in the lower part of the chart, with 19-year-old boys averaging about 166–167 cm in 2019 and girls about 155 cm — matching the table on page 127 exactly, which is a good check that the two sources agree.

What this hints at: if height were fixed entirely by which country you come from, the marks would not have moved in 30 years. They moved a lot — so nutrition, health care and living conditions matter, and they changed fastest in the countries that gained the most.

Careful: every mark on the graph is an average for a whole country. There are short people in the Netherlands and tall people in Timor-Leste. A country average tells you nothing about any one person.

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