Question

Use the box plots comparing the number of male pets and number of female pets attending doggy daycare each day for a month to answer the questions.

Two box plots shown. The top one is labeled Males. Minimum at 1, Q1 at 3, median at 10.5, Q3 at 14, maximum at 21, and a point at 30.

The bottom box plot is labeled Females. Minimum at 0, Q1 at 15, median at 18, Q3 at 21, no maximum shown

Part A: Estimate the IQR for the males' data. (2 points)

Part B: Estimate the difference between the median values of each data set. (2 points)

Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each. (4 points)

Answer 1

The IQR for males is 11, the difference in median values between male and female pets is 7.5, and due to skewness and outliers in the male distribution, the median is a better measure of center for both datasets.

Step-by-step explanation:

Box Plot Analysis

Based on the provided box plots:

• Part A: The interquartile range (IQR) for the males' data is obtained by subtracting Q1 from Q3. Thus, IQR for males = Q3 - Q1 = 14 - 3 = 11.
• Part B: The difference between the median values of male and female pets is calculated by subtracting the median of males from the median of females. Hence, the difference is 18 (females) - 10.5 (males) = 7.5.
• Part C: For males, data has a long tail to the right, implying a positive skew, and there is an outlier at 30. Thus, the median is a better measure of center since it is less affected by this outlier and skewness. Females' data does not show any outliers or extreme skewness, so either the mean or median could be suitable measures of center. However, with no maximum value shown and potentially extreme values, the median remains a safe measure.

Comparisons between male and female attendance distributions can also be derived from the box plots, with the females tending towards a more consistent attendance, reflected in the tighter IQR versus the broader spread for males.