Question

estimating centers quick check
5 of 5
use the image to answer the question.
hours spent playing video games over the weekend
estimate the mean and median of the data in the dot - plot, and then determine which of the following statements is true about the data.
(1 point)
the mean of the data set is greater than the median.
the mean of the data set is less than the median.
the mean of the data set is equal to the median.
the median is 2.5.

Explanation:

Step1: Count data - points

There are 1 + 2+ 3+ 4+ 3+ 2+ 1 = 16 data - points.

Step2: Find median position

For 16 data - points, median is average of 8th and 9th ordered values, which are both 6, so median = 6.

Step3: Estimate mean

Estimated sum: (2×1 + 3×2+ 4×3+ 5×4+ 6×3+ 7×2+ 8×1) = 2 + 6+ 12+ 20+ 18+ 14+ 8 = 80. Mean = $\frac{80}{16}$ = 5.

Answer:

The mean of the data set is less than the median.