Question

19. Calculate standard deviation for the following data

77 73 75 70 72 76 75 72 74 76.​

Answer 1

Answer:

Calculate standard deviation from the following

data:

77, 73, 75, 70, 72, 76, 75, 72, 74, 76

Answer 2

Given,

The numbers.

77 73 75 70 72 76 75 72 74 76

To Find,

The standard deviation of the given numbers.

Solution,

Given that,

Ten numbers are there.

77, 73, 75, 70, 72, 76, 75, 72, 74, 76.

We need to find the standard deviation of these numbers.

First, find out the average.

$\frac{77+73+75+70+72+76+75+72+74+76}{10}$ =74.

Then subtract the average from each number.

77 - 74 = 3

73 - 74 = -1    

75 - 74 = 1

70 - 74 = -4

72 -74 = -2

76 - 74 = 2

75 - 74 = 1

72 - 74 = -2

74 - 74 = 0

76 - 74 = 2  

Then add square of the above numbers.

$3^{2} +(-1)^{2}+ 1^{2}+ (-4)^{2}+(-2)^{2} +2^{2}+1^{2}+ (-2)^{2}+0^{2} +2^{2}$  

= 44.

Variance = 44/9

= 4.9

Therefore standard deviation = $\sqrt{4.9}$

2.21.

Hence, the standard deviation is 2.21for the given numbers.