Question

In order to study the effectiveness of a training program, president kirkman randomly picks 5 employees and records the respective time taken in assembling part k. of the times are 8, 7, 9, 6, and 10 minutes, what is the standard deviation

Answer 1

Answer: The standard deviation of the sample is 1.58.

We calculate the standard deviation as follows:

Let time taken by employees be t

Let the Mean time (average) taken by employees be
`\overline{t}`

t t -
`\overline{t}` (t -
`\overline{t}` )²

8
`8-8 = 0`
`0^(2) = 0`

7
`7-8 = -1`
`-1^(2) = 1`

9
`9-8 = 1`
`1^(2) = 1`

6
`6-8 = -2`
`-2^(2) = 4`

10
`10-8 = 2`
`2^(2) = 4`

Total 40 10

We find the mean or average as follows:

`\overline{t} = (\sum t)/(N)`

`\overline{t} = (40)/(5)`

`\overline{t} = 8`

The formula for calculating the standard deviation of a sample is:

`\sigma_(s) = \sqrt{\frac{\sum (t-\overline{t})^(2)}{N-1}}`

`\sigma_(s) = \sqrt{(10)/(5-1)}`

`\sigma_(s) = \sqrt{(10)/(4)}`

`\sigma_(s) = 1.58113883`