Suppose on a certain test, fifty students earn a perfect score and fifty students earn a zero. determine the mean grade and standard deviation among the one hundred students. a. mean grade among the one hundred students is a0 b. standard deviation: a1

A.

            Mean grade = 50

B.

          Standard deviation= 50

Let us consider the perfect score be 100.

Total number of data points are: 100 ( since there are 50 students)

Score    Number of students

  0                50

100              50

sum of scores or Total score=50×100+50×0=5000.

We know that the mean of the data points is the ratio of sum of the scores to the total number of students

                         Mean=50.

( Since,

)

The standard deviation of a set of data is calculated as follows:

Now, when 50 is subtracted from each entry then we get 50 entries as "-50" ( Since 0-50=-50)

and 50 entries as "50" ( Since 100-50=50 )

Now, on squaring the difference entries we all the 100 entries are 2500 and hence the mean is:

Now on taking the square root we get:

                                     standard deviation=50.

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