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.

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

orchestra answered 1 year ago

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