Question

In independent random samples of 10 men and 10 women, the numbers of minutes spent working out are given by the back-to-back stemplots below:

Part A: Describe the shape of each data set.
Part B: Coraline analyzed the data and stated that the better measure of center for the women is the median. Is Coraline correct? Explain your reasoning.
Part C: Coraline decided there are no outliers in the women's data set. Is she correct? Justify your answer mathematically.

Answer 1

Part A: The men's data is positively skewed, and the women's data is roughly bell-shaped. Part B: Coraline is correct; the median is the better measure of center for the women's data. Part C: We can determine if there are outliers in the women's data by calculating the interquartile range (IQR).

Step-by-step explanation:

Part A: To describe the shape of each data set, we can analyze the stemplots provided. In the stemplot for men, the values are fairly symmetric with a long right tail, which suggests a positively skewed distribution. In the stemplot for women, the values are more symmetric and evenly distributed, resembling a roughly bell-shaped distribution.

Part B: Coraline is correct in stating that the better measure of center for the women's data is the median. The median is less affected by extreme values and is a more robust measure of central tendency when the distribution is skewed or has outliers.

Part C: To determine if there are outliers in the women's data set, we can calculate the interquartile range (IQR). The IQR is the range between the first quartile (Q1) and third quartile (Q3) of the data. If there are any values below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR, they are considered outliers. By performing these calculations on the women's data and examining the stem plot, we can determine if there are any outliers present.