Question

Data on weekday exercise time for 20 females, consistent with summary quantities given in the paper "An Ecological Momentary Assessment of the Physical Activity and Sedentary Behaviour Patterns of University Students" (Health Education Journal [2010]: 116-125), are shown below. Female-Weekday \(\begin{array}{rrrrrr}10.0 & 90.6 & 48.5 & 50.4 & 57.4 & 99.6 \\\ 0.0 & 5.0 & 0.0 & 0.0 & 5.0 & 2.0 \\ 10.5 & 5.0 & 47.0 & 0.0 & 5.0 & 54.0 \\\ 0.0 & 48.6 & & & & \end{array}\) a. Calculate and interpret the values of the median and interquartile range. b. How do the values of the median and interquartile range for women compare to those for men calculated in the previous exercise?

Short answer

Note: Since the exercise does not include data for men, a comparison cannot be made within this solution. However, once the median and interquartile range are found for the men's data, the comparison can be made by examining if the women's median and interquartile range are higher, lower, or the same as men's.

Step-by-step solution

Sort the data in ascending order

The given exercise time data needs to be arranged from smallest to greatest. You can do this manually or you can use a computer tool.

Calculate the Median

Count the observations (n) and find the middle value(s). If n is odd, the median is the middle number. If n is even, the median is the average of the two middle numbers.

Calculate the Interquartile Range

Split the sorted data into two halves. If n is even, split directly in the middle. If n is odd, include the median in both halves. Calculate the median for the lower half to obtain Q1 (the first quartile) and the median for the upper half to obtain Q3 (the third quartile). The interquartile range is Q3 - Q1.