Question 2

This table shows average heights of children from age 5 to 19 over 30 years.

Step 1 — Height changes over time

Let us see how heights changed from 1989 to 2019.

We will choose children at age 10.

First, let us find the boys' height.

This is for age 10 in 1989.

From the table, this is 127.5 cm.

Next, let us find the boys' height.

This is for age 10 in 2019.

From the table, this is 132.6 cm.

The height change for boys is the difference.

$132.6 - 127.5$

$= 5.1$

$\boxed{5.1 \text{ cm}}$

Boys at age 10 grew taller by 5.1 cm.

This happened over 30 years.

Now, let us look at girls at age 10.

Girls' height at age 10 in 1989 is 127.3 cm.

Girls' height at age 10 in 2019 is 132.8 cm.

The height change for girls is the difference.

$132.8 - 127.3$

$= 5.5$

$\boxed{5.5 \text{ cm}}$

Girls at age 10 grew taller by 5.5 cm.

This also happened over 30 years.

So, children generally became taller over these years.

Step 2 — Boys' vs. girls' heights in 2019

Let us compare boys' and girls' heights.

We will use data from the year 2019.

At age 5, boys' height is 107.1 cm.

Girls' height at age 5 is 107.2 cm.

Girls are slightly taller than boys here.

The difference is $107.2 - 107.1 = 0.1$ cm.

At age 12, boys' height is 142.2 cm.

Girls' height at age 12 is 143.8 cm.

Girls are still taller than boys at this age.

The difference is $143.8 - 142.2 = 1.6$ cm.

At age 14, boys' height is 154.4 cm.

Girls' height at age 14 is 150.4 cm.

Now, boys are taller than girls.

The difference is $154.4 - 150.4 = 4.0$ cm.

At age 18, boys' height is 166.0 cm.

Girls' height at age 18 is 155.2 cm.

Boys are much taller than girls at this age.

The difference is $166.0 - 155.2 = 10.8$ cm.

Girls often grow faster at younger ages.

Boys then catch up and become taller later.

Step 3 — Growth between successive ages in 2019

Let us see yearly growth for children in 2019.

The table has two rows for age 16.

We will assume the first '16' row is for age 15.

The second '16' row is for age 16.

First, let us check boys' growth.

From age 12 to age 13, boys' height changes.

It goes from 142.2 cm to 148.4 cm.

The growth is calculated as:

$148.4 - 142.2$

$= 6.2$

$\boxed{6.2 \text{ cm}}$

This is a large growth for boys in one year.

Now, let us check girls' growth.

From age 10 to age 11, girls' height changes.

It goes from 132.8 cm to 138.6 cm.

The growth is calculated as:

$138.6 - 132.8$

$= 5.8$

$\boxed{5.8 \text{ cm}}$

This is a large growth for girls in one year.

Let us also check growth at older ages.

For boys from age 18 to 19, height changes.

It goes from 166.0 cm to 166.5 cm.

The growth is $166.5 - 166.0 = 0.5$ cm.

For girls from age 18 to 19, height changes.

It goes from 155.2 cm to 155.2 cm.

The growth is $155.2 - 155.2 = 0.0$ cm.

Growth slows down a lot after age 17.

Answer

(i) Heights of children generally increased from 1989 to 2019. For example, 10-year-old boys grew by 5.1 cm. 10-year-old girls grew by 5.5 cm. (ii) In 2019, girls were taller than boys at younger ages. For example, at age 12. Boys became taller from age 13 onwards. At age 18, boys were 10.8 cm taller. (iii) In 2019, boys had a big growth spurt around ages 12-13. They grew 6.2 cm in one year. Girls had a big growth spurt earlier. This was around ages 10-11, growing 5.8 cm. Growth slows down a lot after age 17.