Question

the olympic committee wanted to compare the ages of olympic athletes in weight lifting and gymnastics. 20 athletes from both sports were randomly surveyed. the dot plots above show the results of both. what is the difference between the median for both sets?

Explanation:

Step1: Find the median for gymnastics ages

For 20 data - points (an even number of data - points), the median is the average of the 10th and 11th ordered data - points. Counting the dots in the gymnastics dot - plot, the 10th and 11th values are both 16. So the median for gymnastics, $M_{g}=16$.

Step2: Find the median for weight - lifting ages

For 20 data - points (an even number of data - points), the median is the average of the 10th and 11th ordered data - points. Counting the dots in the weight - lifting dot - plot, the 10th value is 23 and the 11th value is 24. So the median for weight - lifting, $M_{w}=\frac{23 + 24}{2}=23.5$.

Step3: Calculate the difference between the medians

The difference $\Delta M=\vert M_{w}-M_{g}\vert=23.5−16 = 7.5$.

Answer:

7.5