Chapter 2, Problem 8P

Explanation of Solution

Given: The following table:

To find: The possible way to normalize the data.

Solution:

The normalization can be calculated by subtracting the average by each measurement and dividing the difference with the standard deviation. The mean value of age will be 44.67. The mean value of income will be 98666.67. The standard deviation’s value for the age will be 13.65. The standard deviation’s value for the income will be 62867.06. The formula for calculating the mean as well as standard deviation is as follows:

$\text{Mean = }\frac{\text{Sum of all terms}}{\text{Total number of terms}}$

$\text{Standard deviation = }\sqrt{\frac{{\displaystyle \sum {\left(x_i-\mu \right)}^2}}{N}}$

The calculation for the mean value of age is as follows:

$\begin{array}{l}\text{Mean = }\frac{25+56+65+32+41+49}{6}\\ =44.67\end{array}$

The calculation for the mean value of income is as follows:

$\begin{array}{l}\text{Mean = }\frac{49000+156000+99000+192000+39000+57000}{6}\\ =98666.67\end{array}$

The calculation of the standard deviation value for age is as follows:

$\begin{array}{l}\text{Mean = }\frac{49000+156000+99000+192000+39000+57000}{6}\\ =98666\end{array}$