What is the mean score for the $20$ rolls?

Question

A fair die is rolled twenty times. The results are shown in the bar graph. What is the mean score for the $20$ rolls?

Answer 1

You have three 1s, one 2, five 3s, one 4, four 5s and six 6s so you want to find the mean (average) of

$$\{1,1,1,2,3,3,3,3,3,4,5,5,5,5,6,6,6,6,6,6\}.$$

As Gerry Myerson essentially asked, can you find the average of these numbers?

Answer 2

Hint: Mean $\displaystyle =\frac{\sum_{\text{over all score}} [\text{(frequency) }\times score]}{\sum_{\text{over all score}} \text{(frequency) }}$

Answer 3

Hint Write down (using the graph) how many rolls of each score happened. In total, you wil now know which scores $x_1,\ldots,x_{20}$ were rolled in the 20 rolls.

Now find the arithmetic mean $\frac{1}{20} \sum_{k=1}^{20} x_k$ and it will be your mean score.