In a statistics class of 100 students, the mean score on the midterm was 98. In another class of 23 students, the mean score was 8. What was the mean score of the two classes combined?

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Answer 1 · 2016-09-07T07:54:44

$Mean = \frac{9984}{123} = 81.2$ $"Mean" = 9984/123 = 81.2$

When we are finding a mean, we need to know:
the sum of all the values, and how many values there are.

$Mean = \frac{Total}{Number}$ $"Mean" = "Total"/"Number"$

However, if we already know the Mean and Number, we can find the total.

$Total = Mean \times Number$ $"Total = Mean" xx "Number"$

Note: You can ADD TOTALS, and NUMBERS, but you may not add means.

For the class of 100 students with a mean of 98:

$Total = 98 \times 100 = 9800$ $"Total" = 98 xx 100 = 9800$

For the class of 23 students, the mean was 8.

$Total = 8 \times 23 = 184$ $"Total" = 8xx23 = 184$

Now combine the two groups:

There are $100 + 23 = 123 students altogether$ $100+23 = 123 " students altogether"$ .

The total is: $9800 + 184 = 9984$ $9800+184 = 9984$

$Mean = \frac{9984}{123} = 81.2$ $"Mean" = 9984/123 = 81.2$