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
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,
[tex]Mean=\dfrac{5000}{100}=50[/tex] )
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:
[tex]Variance=\dfrac{2500\times 100}{100}\\\\\\Variance=2500[/tex]
Now on taking the square root we get:
standard deviation=50.
