Question

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

Answer 1

The mean is 50 because if half get a "100" and the other half get a "0" the mean is 50. The standard deviation is 7.07 when you plug this into the 1-VARS stats on a calculator after putting this data in L1 List data set on the calculator.

a. 50

b. 7.07

Answer 2

A.

Mean grade = 50

B.

Standard deviation= 50

Explanation:

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,

`Mean=(5000)/(100)=50` )

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

• subtract mean from every entry.

• square the above difference entries

• Take it as new entry and calculate the mean of the new data entry.

• lastly take the square root of the mean so calculated.

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:

`Variance=(2500* 100)/(100)\\\\\\Variance=2500`

Now on taking the square root we get:

standard deviation=50.