Question
In: Statistics and Probability
Imagine there are five students in a class. Their scores on the midterm exam are: 93,...
Imagine there are five students in a class. Their scores on the midterm exam are: 93, 85, 70, 78, and 64. Calculate the mean, the variance and the standard deviation and interpret the meaning of the variance and standard deviation.
Solutions
Expert Solution
Solution:
| x | x2 |
| 93 | 8649 |
| 85 | 7225 |
| 70 | 4900 |
| 78 | 6084 |
| 64 | 4096 |
 x
= 390 |
x2
= 30954 |
a ) The sample mean is 
Mean
= (x
/ n) )
= (93 +85 + 70 + 78 + 64 / 5 )
= 390 / 5
= 15.5
Mean
= 15.5
b ) The sample variance is S2
S2 = (
x2 ) - ((
x)2 / n ) n -1
= (30954 ( (390 )2 / 5 ) 4
= ( 30954 - 30420 / 4)
= (534 / 4)
= 133.5
The sample variance = 133.5
c ) The sample standard deviation is S = 
sample variance
=
133.5
= 11.5542
The sample standard deviation is S = 11.5542
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