Question

Find the mean, median and mode for the following scores.

Test scores
90
80
70
60
50
Frequency
2
3
10
5
2
O mean = 69.09; median = 90; mode= 60
O mean = 69.09, median = 70; mode= 70
O mean = 2.00, median = 70; mode = 60
O mean = 70.09; median = 70, mode = 70

Answer 1

(b) mean 69.09, median 70, mode 70

Explanation:

You want the mean, median, and mode of the given distribution of test scores.

Mode

The mode is the score that has the greatest frequency. That score is 70, with a frequency of 10. (Eliminates choices A and C.)

The mode is 70.

Median

There area a total of 2+3+10+5+2 = 22 test scores, so the median will be the average of the 11th and 12th scores. Both of these are 70, so the median is 70.

Mean

There are more scores below 70 (7) than above 70 (5), so the mean is less than 70. (Eliminates choice D.)

The test score statistics are ...

mean = 69.09; median = 70; mode = 70 . . . . . matches choice B

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Additional comment

For the purpose of this problem, we do not need to find the exact mean, but it is not difficult to do so. The distribution is symmetrical about 70 but for the fact that there are 2 unbalanced scores of 60. This tells you the mean will be below 70. The amount below can be computed like this:

(20·70 +2·60)/22 = (22·70 +2(70 -10))/22

= 70 -20/22 = 70 -0.91 = 69.09 . . . . mean of the data set

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