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

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

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"mean" is just a fancy word for "average". What do you know about computing the average of a bunch of numbers? – Gerry Myerson Jun 18 '13 at 13:50
I don't will you please guide me . – SSK Jun 18 '13 at 14:06
It seems from your comment on one of the answers that you do know something about computing the average of a bunch of numbers. Good on ya. – Gerry Myerson Jun 19 '13 at 9:04

## 3 Answers

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?

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my pleasure , $1+1+1+2+3+3+3+3+3+4+5+5+5+5+6+6+6+6+6+6/20 = 4$ – SSK Jun 18 '13 at 14:16
Boom. This is where Abhra's formula comes from and is exactly what gt has although I wasn't sure if you understood the sigma notation; the $\sum$ just means 'add up'. – Jp McCarthy Jun 18 '13 at 14:59

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

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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.

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