Question

Use the side-by-side boxplots shown to complete parts (a) through (e). Q X у 30 90 (a) What is the median of variable x? The median of variable xis (Round to the nearest integer as needed.) (b) What is the third quartile of variable ? The third quartile of variable y s . (Round to the nearest integer as needed.) (c) Which variable has more dispersion? Why? O A. Variable y—the range of variable x is smaller than that of variable y OB. Variable x-the interquartile range of variable x is larger than that of variable y OC. Variable x-the range of variable y is smaller than that of variable x. D. Variable y—the interquartile range of variable y is larger than that of variable x. O E. Both dispersions are equal. (d) Describe the shape of the variable x. Support your position. Choose the correct answer below. O A Symmetric—the median is the center of the box and the left and right whiskers are about the same length. B. Skewed left—the median is left of center in the box and the left whisker is longer than the right whisker. OC. Skewed right—the median is right of center in the box and the left whisker is shorter than the right whisker. OD. There is not enough information to determine the shape of the variable x (e) Describe the shape of the variable y. Support your position. Choose the correct answer below. A. Skewed right—the median is left of center in the box and the left whisker is shorter than the right whisker. OB. Symmetric-the median is the center of the box and the left and right whiskers are about the same length. OC. Skewed left—the median is right of center in the box and the left whisker is longer than the right whisker. OD. There is not enough information to determine the shape of the variable y

Answer 1

The two boxplots of X and Y are compared side by side.

We note that the middle line of the box of the X boxplot is pointed near the point 80.

So, the median of X is 80.

We also note that the ending line of the box in the Y boxplot is pointed near 100.

So, the third quartile of Y is 100.

Now, we note that variable X stretches from 50 to 110 approximately. But variable Y stretches from 0 to 120.

So, the correct answer of c) is option A) Variable Y, because the range of variable X is smaller than that of variable Y.

Now, the variable X is

option A) Symmetric, because the median is at the middle of the box, and the whiskers are of almost same length.

Now, the variable Y is

option C) Skewed left, because the median is right to the centre of the box and the left whisker is longer.