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The graph compares shoe sizes for a group of 100 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

15
15

16
16

35
35

50

1 answer

To analyze how many more two-year-old boys have a shoe size of 6 or less compared to the three-year-old boys, we will look at the information given for the two groups based on the box and whisker plots.

  1. Two-year-old boys:

    • Median shoe size is 6.
    • The lower quartile (25th percentile) is 3.5, and the upper quartile (75th percentile) is 7.5.
    • Thus, at least 25% of the two-year-old boys have a shoe size of 3.5 or less.
    • Since the median is 6, we can expect that around 50% of the group (which is 100 boys) have a shoe size of 6 or less.
    • Therefore, about 50 boys (50% of 100) have a shoe size of 6 or less.

  2. Three-year-old boys:

    • Median shoe size is 8.
    • The lower quartile is 6.5, and the upper quartile is 9.5.
    • This indicates that around 25% of the three-year-old boys have a shoe size of 6.5 or less.
    • Since the median is 8, it indicates that less than 50% of the group has a shoe size of 6 or less. Specifically, it's reasonable to estimate that about 25% of them do, which is about 15 boys (25% of 60).

Now, calculating the difference between the two groups:

  • Two-year-old boys with shoe size 6 or less: 50
  • Three-year-old boys with shoe size 6 or less: 15

Thus, the difference is:

50 (two-year-olds) - 15 (three-year-olds) = 35.

So, the answer is 35.