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Chapter 2: Q 22. (page 107)

Step right up! A dot plot of the distribution of height for Mrs. Navard鈥檚 class is shown, along with some numerical summaries of the data.

Suppose that Mrs. Navard has the entire class stand on a 6-inch-high platform and then asks the students to measure the distance from the top of their heads to the ground.

a. What shape would this distribution of distance have?

b. Find the mean and median of the distribution of distance.

c. Find the standard deviation and interquartile range (IQR) of the distribution of distance.

Short Answer

Expert verified

Part (a) Right skewed.

Part (b) Mean =67inch

Median =66inch

Part (c) Standard deviation =4.29

Interquartile range =7

Step by step solution

01

Part (a) Step 1: Given information

02

Part (a) Step 2: Explanation

The form of the given distribution is positively skewed or right-skewed, as evidenced by the provided dot plot. The tail of the distribution appears to be on the right side. Furthermore, the mean is greater than the median, indicating the same because the mean is greater than the median when the data is right-skewed.

03

Part (b) Step 1: Explanation

The mean of the distance data is 67inches and the median is 66inches according to the facts provided.

04

Part (c) Step 1: Explanation

According to the data's statistics, the standard deviation is 4.29inchand the interquartile range is the difference between the data's third and first quartiles. The first quartile score is 63while the third quartile score is 70

Therefore, the interquartile range =70鈭�63=7

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