Chapter 10.3, Problem 10PPS

To determine

To calculate standard deviation of the given data set.

Answer to Problem 10PPS

Standard deviation is 4.35

Explanation of Solution

Given information: Data points are

76, 78, 81, 75, 80, 80, 76, 77

Formula used: Mean formula is,

Mean= $\frac{{\displaystyle \sum _{i=1}^n{X}_i}}{n}$

Where, n=total number of terms,

  ${\displaystyle \sum _{i=1}^n{X}_i}$ = sum of all terms Standard deviation is,

  ${\sigma }_{}=\sqrt{\frac{{\displaystyle \sum _{}^{}{(x_i^{}-\mu )}^2}}{N}}$

Where $x_i^{}$ = each value from data

  $\mu$ =mean of data

  $N$ = size of data

Calculation:

For mean,

Substituting values,

  $=\frac{76+78+81+75+80+80+76+77}{8}$

So,

  $=\frac{623}{8}$

On solving,

  $=77.85$

Hence, mean is 77.85

For standard deviation,

Values	Difference= $x_{}^{}-\mu$	${(x_{}^{}-\mu )}^2$
76	-1.8	3.51
78	0.12	0.015
81	3.1	9.76
75	-2.87	8.26
80	2.12	4.51
80	2.12	4.51
76	-1.87	3.51
77	-0.87	0.76
Total		34.87

Substituting the values in standard deviation formula,

  $=\sqrt{\frac{34.87}{8}}$

On solving,

  $=4.35$

Hence, Standard deviation is 4.35