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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?

1 answer

To determine how many more two-year-old boys have a shoe size of 6 or less compared to the three-year-old boys, we can refer to the box and whisker plots’ characteristics and the information provided.

  1. Two-Year-Old Boys:

    • The median shoe size for the two-year-old boys is 6.
    • The lower quartile (Q1) is at 3.5, and the upper quartile (Q3) is at 7.5.
    • Since the lower quartile is 3.5 and the median is 6, we can infer that a significant proportion of two-year-old boys have shoe sizes of 6 or less. This includes all sizes from the minimum (3) to the median (6).

  2. Three-Year-Old Boys:

    • The median shoe size for the three-year-old boys is 8.
    • The lower quartile (Q1) is at 6.5.
    • This indicates that shoe sizes at or below 6 are mostly below the lower quartile, suggesting that fewer three-year-old boys have shoe sizes of 6 or less.

Given that:

  • The two-year-old boys have shoe sizes distributed from 3.5 up to their median at 6, it can be assumed a significant number of them are at size 6 or lower. Since there are 80 two-year-old boys, a reasonable estimation would be around 50 boys (or more) having shoe sizes of 6 or lower.

  • The three-year-old boys, with their lower quartile at 6.5 and the median at 8, would likely mean that only a few, potentially 10-15 boys, have shoe sizes of 6 or lower out of the total 60.

Based on these estimates, let's calculate:

  • Two-year-old boys with shoe size of 6 or less: approximately 50 or more.
  • Three-year-old boys with shoe size of 6 or less: approximately 10-15.

Subtracting these estimates gives:

  • If we take the estimate of 50 for the two-year-olds minus 15 for the three-year-olds gives approximately 35 more two-year-old boys with shoe sizes of 6 or lower compared to three-year-olds.

Thus, the answer to the question is that there are about 35 more two-year-old boys who have a shoe size of 6 or less compared to the three-year-old boys.