Question

Six students from a statistics class reported the number of hours of television they watch per week. Here are their data: 8, 10, 5, 14, 3, 6. What is the standard deviation of the number of hours of television watched per week for this sample of six students?

Answer 1

3.93

Explanation:

Let x is the number of hours of television watched per week by six students.

X 8 10 5 14 3 6

Standard deviation for sample data is

`Standard deviation=S=\sqrt\frac{{sum(x-xbar)^2} }{n-1}`

`xbar=(sum(x))/(n)`

`xbar=(8+10+5+14+3+6)/(6)`

`xbar=(46)/(6)`

xbar=7.67

`sum(x-xbar)^2=(8-7.67)^2+(10-7.67)^2+(5-7.67)^2+(14-7.67)^2+(3-7.67)^2+(6-7.67)^2`
`sum(x-xbar)^2=0.11+5.44+7.11+40.11+21.78+2.78=77.33`

`Standard deviation=S=\sqrt\frac{{(77.33)} }{5}`

`S=\sqrt15.466`

S=3.93