This graph compares shoe sizes for a group of 80 two-year-old boys and a group of 60 three-year-old boys.

Two box and whisker plots showing shoes sizes on a number line from 2.5 to 13. The upper plot represents the group of 2 year-old boys. For this upper plot, the minimum number is 3, the maximum number is 9.5, the right side of the box is 7.5, the left side of the box is 3.5, and the bar in the box is at 6. The lower plot represents the group of 3 year-old boys. For this lower plot, the minimum number is 5, the maximum number is 11.5, the right side of the box is 9.5, the left side of the box is 6.5, and the bar in the box is at 8.

About how many more two-year-old boys have a shoe size of 6 or less, compared to the three-year-old boys?

Responses

6
6

15
15

25
25

40

1 answer

To analyze the shoe sizes of the two groups of boys, we can summarize the information presented in the box and whisker plots for the two-year-old and three-year-old boys.

Two-year-old boys:
- Minimum: 3
- Maximum: 9.5
- Lower quartile (Q1): 3.5
- Upper quartile (Q3): 7.5
- Median: 6
Three-year-old boys:
- Minimum: 5
- Maximum: 11.5
- Lower quartile (Q1): 6.5
- Upper quartile (Q3): 9.5
- Median: 8

From the box plots, we can infer the distribution of shoe sizes. The two-year-old boys have a range of shoe sizes from 3 to 9.5, while the three-year-old boys have a range from 5 to 11.5.

To find out how many two-year-old boys have shoe sizes of 6 or less, we note the following:

The maximum shoe size that two-year-old boys have is 9.5, indicating some boys have larger sizes than 6.
The median shoe size for two-year-old boys is 6, and since we are only assessing the number of boys with shoe sizes of 6 or less, we can assume that a significant portion of them do.

For the three-year-old boys:

Their minimum shoe size starts at 5 and goes up, indicating that fewer of these boys will have a shoe size of 6 or less.

However, without specific counts from the data, we can estimate as follows:

Generally, you could expect that more than half of the two-year-old boys (which is likely 80 boys) would have sizes 6 or less, given that the median is 6.
The three-year-old boys (60 boys) will likely have a smaller percentage with sizes 6 or less, considering their quartiles.

Now, if we were to make a reasonable estimate, we could say that about:

Around 50% (or 40 boys) of the two-year-olds could have sizes of 6 or less.
Only about 25% (or 15 boys) of the three-year-olds could have sizes of 6 or less.

Putting this into calculation:

Two-year-olds with sizes of 6 or less: approximately 40
Three-year-olds with sizes of 6 or less: approximately 15

The difference is: 40 - 15 = 25

Thus, the number of two-year-old boys with a shoe size of 6 or less compared to three-year-old boys is approximately 25.

So, the correct choice is: