Question

The following data are the distances from the workplace (in miles) for the 5 employees of a small business.

Answer 1

1. Given that the population data is : 15,5,8,2,5

• number of sample in data , ,n = 5

,

• Mean = sum of sample in the data / number of sample

= (15+5+8+2+5)/5

= 35/5

Therefore mean = 7

2. Calculate varience as in the box below:

`\begin{gathered} _{}\text{Varience = }(1)/(n)\mleft\lbrace(x_i-\vec{x}\mright)^2 \\ \text{ = }(1)/(5)\mleft\lbrace(7-15)^2+(7-5)^2+(7-8)^2+(7-2)^2+(7-5)^2\mright\rbrace \\ \text{ = }(1)/(5)\mleft\lbrace(-8^2\mright)+(-2)^2+(-1^2)+(5^2)+(2^2)\} \\ \text{ =}(1)/(5)\mleft\lbrace64\text{ + 4+ 1 +25+4}\mright\rbrace \\ \text{ = }(1)/(5)(98) \\ \text{ = }(98)/(5) \\ \therefore S\tan dard\text{ deviation = }\sqrt[]{varience\text{ }} \\ \text{ = }\sqrt[]{(98)/(5)}\text{ } \\ \text{ =4.427} \end{gathered}`

• This means that Standard deviation = 4.43