Question

Unit sales for new product ABC have varied in the first seven months of this year as follows: Month Jan Feb Mar Apr May Jun Jul Unit Sales 148 329 491 167 228 285 441 What is the (population) standard deviation of the data

Answer 1

`\sigma = 121.53`

Explanation:

Required

The population standard deviation

First, calculate the population mean

`\mu = (\sum x)/(n)`

This gives:

`\mu = (148+ 329+ 491 +167+ 228+285+ 441)/(7)`

`\mu = (2089)/(7)`

`\mu = 298.43`

The population standard deviation is:

`\sigma = \sqrt{(\sum(x - \bar x)^2)/(n)}`

So, we have:

`\sigma = \sqrt{((148 - 298.43)^2 + ..........+ (441- 298.43)^2)/(7)}`

`\sigma = \sqrt{(103387.7143)/(7)}`

`\sigma = √(14769.6734714)`

`\sigma = 121.53`