Question

select the correct answer.
the ages of the people who attend a weekly yoga class at the local yoga studio are shown in the table below.
43 52 35 27 26 51 48 36
42 37 62 44 50 26 40 30
which data display(s) can be used to find the median for the ages of the yoga students?
i. box plot
ii. dot plot
iii. histogram
a. i, ii, and iii
b. i and ii
c. i only
d. ii and iii

Explanation:

Step1: Analyze box plot

A box - plot (box - and - whisker plot) has a line inside the box that represents the median. So, we can directly read the median from a box - plot.

Step2: Analyze dot plot

A dot - plot shows each data point. We can list the data points in order (by counting the dots) and then find the median. For example, if we have \(n\) data points, and \(n = 16\) (since there are \(8 + 8=16\) data points in the table). If \(n\) is even, the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered data points. We can order the data using a dot - plot.

Step3: Analyze histogram

A histogram groups data into intervals. It does not show individual data points clearly enough to order all the data points (required for finding the median when \(n\) is small). For example, if two different histograms have the same interval frequencies but different data point distributions within the intervals, the median can be different. We cannot accurately find the median from a histogram.

Answer:

B. I and II