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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?

Respuesta :

To determine about how many more boys have a shoes size of 6 or less, you need to understand that a box and whisker plot takes a data set and show it in quarters (25% of the data is represented in each section).

For the 2 years olds, if the box in the middle, that means that half of the boys have a shoe size at 6 or under.  There were 80 boys chosen for this study, so half of that is 40.

For the 3 year olds, the closest point to 6 is 6.5, and it is located after the line on the left.  This means that only 25% of the boys have shoe sizes of 6.5 or under.  25% of the 60 three-year olds they collected data on is 15.

The difference is 40-15= 25.
There are about 25 more two-year olds wearing a size 6 or under.

About 25 more two-year-old boys have a shoe size of 6 or less, compared to the three-year-old boys.

How does a boxplot shows the  data points?

A box plot has 5 data description.

  1. The leftmost whisker shows the minimum value in the data.
  2. The rightmost whisker shows the maximum value in the data.
  3. The leftmost line in the box shows the first quartile.
  4. The middle line shows the median, also called second quartile.
  5. The last line of the box shows the third quartile.

We're specified that:

For two-years-old boys:

  • Total count = 80
  • Minimum number = 3
  • Maximum number is 9.5,
  • the right side of the box is 7.5 (third quartile),
  • the left side of the box is 3.5 (first quartile), and
  • the bar in the box is at 6 (second quartile or median).

For three-years-old boys:

  • Total count = 60
  • Minimum number = 5
  • Maximum number is 11.5,
  • the right side of the box is 9.5 (third quartile),
  • the left side of the box is 6.5 (first quartile), and
  • the bar in the box is at 8 (second quartile or median).

From data of 2-years-old boys, the size 6 is the median. That means, there are approx 50% boys on either of this 6 shoe size.

50% of 80 is 40.

So 40 two-years-old boys have shoe size 6 or less,

and another 40 two-years-old boys have shoe size 6 or more.

From data of 3-years-old boys, the size 6 is less than 6.5 which is first quartile. First quartile has approx 25% observation on its left, and 75% on right.

Left side is smaller or equal (the data is in ascending order, as visible that first quartile < third quartile) to 6.5, and right is bigger or equal to 6.5.

Now, we can take 6.5 approx 6, and therefore, 25% of three-years-old boys have  a shoe size of 6 or less,.

25% of 60 is 60/4 = 15

Thus, approx 15 three-years-old boys have a shoe size of 6 or less.

The difference between both counts is: 40-15 = 25

Thus, about 25 more two-year-old boys have a shoe size of 6 or less, compared to the three-year-old boys.

Learn more about box-plot here:

https://brainly.com/question/1523909