Question

For the data set: 0.09, 0.10, 0.11, 0.13, 0.09, 0.11, 0.10, 0.07 To obtain information of the precision of the data set the standard deviation would be:

a. 0.018
b. 0.022
c. 0.0166
d. 0.01

Answer 1

Answer:

Option A is correct (0.018)

S.D≅0.018

Explanation:

Option A is correct (0.018)

General Formula for Standard Deviation is:

$Standard\ Deviation=\sqrt{\frac{\sum_{i=1}^{n}(x_{i}-\bar x)^2}{n-1}}$

Where:

$x_{i}$ is the data value

$\bar x$ is the mean/average of data

n is the total number of data elements

Calculating $\sum_{i=1}^{n}(x_{i}-\bar x)^2}$

$\bar x=\frac{0.09+0.10+ 0.11+ 0.13+ 0.09+ 0.11+ 0.10+0.07}{8} \\\bar x=0.1$

$\sum_{i=1}^{n}(x_{i}-\bar x)^2}=(0.09-0.1)^2+(0.1-0.1)^2+(0.11-0.1)^2+(0.13-0.1)^2+(0.09-0.1)^2+(0.11-0.1)^2+(0.1-0.1)^2+(0.07-0.1)^2\\\sum_{i=1}^{n}(x_{i}-\bar x)^2}=2.2*10^{-3}$

Calculating n-1:

Total number of terms=8

n-1=8-1=7

Standard Deviation is:

$S.D=\sqrt{\frac{2.2*10^{-3}}{7}}\\S.D=0.0177$

S.D≅0.018