Question

The frequency table shows the scores from rolling a dice 10 times work out the mean

Answer 1

Answer:   3.8

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Explanation:

For each row, multiply the values straight across.

• Row one: 1*1 = 1
• Row two: 2*3 = 6
• Row three: 3*0 = 0
• Row four: 4*2 = 8
• Row five: 5*1 = 5
• Row six: 6*3 = 18

The list of products we got were: 1, 6, 0, 8, 5, 18

Add up those products to get: 1+6+0+8+5+18 = 38

The value 38 represents the total value if we were to add up all of the results of each die roll (it shows up again in the next section). We divide this over the total frequency, which is the sum of everything in the second column. That total frequency being 1+3+0+2+1+3 = 10.

So the mean is 38/10 = 3.8

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A longer way to do this is to expand each value based on the frequency shown. The value '1' shows up one time, so we just write "1" once. The value "2" shows up three times, so we write "2" three times. So far the list is {1,2,2,2}

The value "3" doesn't show up at all, so we skip to "4" which shows up twice. The updated data set so far is {1,2,2,2,4,4}

Then it updates again to {1,2,2,2,4,4,5} when we account for the single "5"

Finally, the fully up to date list of values is {1,2,2,2,4,4,5,6,6,6}

Computing the mean of this set has us add up the values to get 1+2+2+2+4+4+5+6+6+6 = 38. We have that "38" show up again, which is not a coincidence. We divide over 10 because there are ten values in the fully up to date list shown above. So this is a different method to get the mean of 3.8

If you prefer this second method, then you should use it; however, I recommend the first method as it's faster and more efficient. It might be handy to try both methods just for practice.