Question

Step right up! A dot plot of the distribution of height for Mrs. Navard’s 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

Part (a) Right skewed.

Part (b) Mean $=67inch$

Median $=66inch$

Part (c) Standard deviation $=4.29$

Interquartile range $=7$

Step-by-step solution

Part (a) Step 1: Given information

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.

Part (b) Step 1: Explanation

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

Part (c) Step 1: Explanation

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

Therefore, the interquartile range $=70-63=7$