Question

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 2, 6, 15, 9, 11, 22, 1, 4, 8, 19

Answer 1

Answer:

6.7

Step-by-step explanation:

The given data set is

2, 6, 15, 9, 11, 22, 1, 4, 8, 19

We need to find the standard devision of the data.

Formula for mean:

$Mean=\dfrac{\text{Sum of observations}}{\text{Number of observations}}$

$Mean=\dfrac{2+6+15+9+11+22+1+4+8+19}{10}$

$Mean=\dfrac{97}{10}$

$Mean=9.7$

Fomula for standard deviation:

$\text{Standard deviation}=\sqrt{\dfrac{\sum (x-\overline{x})^2}{n}}$

$\sum (x-\overline{x})^2=(2-9.7)^2+(6-9.7)^2+(15-9.7)^2+(9-9.7)^2+(11-9.7)^2+(22-9.7)^2+(1-9.7)^2+(4-9.7)^2+(8-9.7)^2+(19-9.7)^2=452.1$

$\text{Standard deviation}=\sqrt{\dfrac{452.1}{10}}$

$\text{Standard deviation}=\sqrt{45.21}$

$\text{Standard deviation}=6.72383818961$

$\text{Standard deviation}\approx 6.7$

Therefore, the standard deviation is 6.7.