Answer:
Standard deviation is 7.16
Step-by-step explanation:
We have given a set of numbers :
73, 76, 79, 82, 84, 84, 97
To calculate the standard deviation of the given data set, first we have to work out the mean.
Mean = [tex]\frac{(73+76+79+82+84+84+97)}{7}[/tex]
= [tex]\frac{575}{7}[/tex] = 82.14
Now for each number subtract the mean and square the result
(73 - 82.14)² = (-9.14)² = 83.54
(76 - 82.14)² = (-6.14)² = 37.70
(79 - 82.14)² = (-3.14)² = 9.86
(82 - 82.14)² = (0.14)² = 0.02
(84 - 82.14)² = (1.86)² = 3.46
(84 - 82.14)² = (1.86)² = 3.46
(97 - 82.14)² = (14.86)²= 220.82
Now we calculate the mean from of those squared differences :
Mean = [tex]\frac{83.54+37.70+9.86+0.02+3.46+3.46+220.82}{7}[/tex]
= [tex]\frac{358.86}{7}[/tex]
= 51.27
Now square root of this mean = standard deviation = √51.27 = 7.16
Therefore, Standard deviation is 7.16
