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

Answer:

$\sigma = 121.53$

Step-by-step explanation:

Required

The population standard deviation

First, calculate the population mean

$\mu = \frac{\sum x}{n}$

This gives:

$\mu = \frac{148+ 329+ 491 +167+ 228+285+ 441}{7}$

$\mu = \frac{2089}{7}$

$\mu = 298.43$

The population standard deviation is:

$\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}$

So, we have:

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

$\sigma = \sqrt{\frac{103387.7143}{7}}$

$\sigma = \sqrt{14769.6734714}$

$\sigma = 121.53$