Question 40
Which of the following statements can be justified using the data?
- The average heights of both boys and girls at every age increased from 1989 to 2019.
- The average height of 13-year-old girls in 1989 is more than the average height of 14-year-old girls in 2009.
- The average height of 15-year-old boys in 2019 is more than the average height of 16-year-old boys in 1989.
- All girls aged 13 are taller than all girls aged 11.
- Throughout the age period 5 to 19, the average boy's height is more than the average girl's height.
- Boys keep growing even beyond age 19.
We will check each statement by looking at the average height data in the table.
Step 1 — Understanding the Data Table
Let us look at the table. It shows average heights in centimeters. The first column shows the age in years. For each year, there are two height values. The first height value is for boys. The second height value is for girls. We will use these values to check each statement.
Step 2 — Evaluating Statement 1
Statement 1 says average heights of both boys and girls increased from 1989 to 2019 for every age. Let us compare the average height for boys at each age. We compare the 1989 boy's height with the 2019 boy's height. For example, for boys at age 5: Boy's height in 1989 is 101.3 cm. Boy's height in 2019 is 107.1 cm. This shows an increase. We check this for all ages from 5 to 19. For every age, the boy's height in 2019 is greater than in 1989. Let us compare the average height for girls at each age. We compare the 1989 girl's height with the 2019 girl's height. For example, for girls at age 5: Girl's height in 1989 is 100 cm. Girl's height in 2019 is 107.2 cm. This shows an increase. We check this for all ages from 5 to 19. For every age, the girl's height in 2019 is greater than in 1989. So, statement 1 is justified.
Step 3 — Evaluating Statement 2
Statement 2 compares 13-year-old girls in 1989 and 14-year-old girls in 2009. Average height of 13-year-old girls in 1989 is 143.2 cm. Average height of 14-year-old girls in 2009 is 148 cm. Let us compare these two heights. This comparison is false. So, statement 2 is not justified.
Step 4 — Evaluating Statement 3
Statement 3 compares 15-year-old boys in 2019 and 16-year-old boys in 1989. Average height of 15-year-old boys in 2019 is 159 cm. Average height of 16-year-old boys in 1989 is 158.9 cm. Let us compare these two heights. This comparison is true. So, statement 3 is justified.
Step 5 — Evaluating Statement 4
Statement 4 talks about "all girls". The table provides only average heights. Average height does not mean every single person. We cannot conclude about individual heights from averages. So, statement 4 is not justified.
Step 6 — Evaluating Statement 5
Statement 5 says boys are always taller than girls from age 5 to 19. We need to check if boy's height is always more than girl's height. Let us look at age 11 in 1989. Average height of 11-year-old boys in 1989 is 132.2 cm. Average height of 11-year-old girls in 1989 is 133.4 cm. Here, the boy's height is less than the girl's height. This shows the statement is false. So, statement 5 is not justified.
Step 7 — Evaluating Statement 6
Statement 6 says boys keep growing even beyond age 19. The table only shows data up to age 19. There is no information for ages older than 19. We cannot make conclusions beyond the given data. So, statement 6 is not justified.
Answer
(1) The average heights of both boys and girls at every age increased from 1989 to 2019. (3) The average height of 15-year-old boys in 2019 is more than the average height of 16-year-old boys in 1989.
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- The average heights of both boys and girls at every age increased from 1989 to 2019.
- The average height of 13-year-old girls in 1989 is more than the average height of 14-year-old girls in 2009.
- The average height of 15-year-old boys in 2019 is more than the average height of 16-year-old boys in 1989.
- All girls aged 13 are taller than all girls aged 11.
- Throughout the age period 5 to 19, the average boy's height is more than the average girl's height.
- Boys keep growing even beyond age 19.
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