Question

1. draw a dot - plot of a data distribution representing the ages of 20 people for which the median and the mean are approximately the same value. explain your reasoning.

Explanation:

Step1: Recall mean - median relationship

In a symmetric distribution, the mean and median are approximately equal.

Step2: Create dot - plot for symmetric data

We can create a dot - plot where the data is symmetrically distributed around a central value. For example, assume the ages are symmetrically distributed around 30. We can have values like 25, 26, 27, 28, 29, 30, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 37. Place dots above each age value on a number line.

Step3: Explain reasoning

Since the data is symmetrically distributed around a central value, the sum of the deviations of the data points below the central value from the central value is approximately equal to the sum of the deviations of the data points above the central value from the central value. So, the mean (which is the sum of all values divided by the number of values) and the median (the middle value for an even - numbered data set, or the average of the two middle values) will be approximately the same.

Answer:

Create a symmetric dot - plot of ages (example values given above) around a central value. Reason: In symmetric data distributions, the mean and median are approximately equal due to balanced deviations around the central value.