Question

The monthly salaries of the three people working in a small firm are $3,500, $4,000, and $4,500. Suppose the firm makes a profit and everyone gets a $100 raise. How, if at all, would the standard deviation of the three salaries change? The standard deviation would stay the same. The standard deviation would increase. The standard deviation would decrease. Cannot be answered without doing calculations.

Answer 1

The standard deviation would stay the same

Step-by-step explanation:

Given:

Salaries as:

$3,500

$4,000

$4,500

and after $100 raise

$3,600

$4,100

$4,600

The average of the salaries before raise

= ( $3,500 + $4,000 + $4,500 ) / 3 = $4,000

The standard deviation =
`\sigma=\sqrt{((mean-x_i)^2)/(n)}`

and

`\sigma=\sqrt{((4,000-3500)^2+(4,000-4000)^2+(4,000-4500)^2)/(3)}`

or

`\sigma=\sqrt{(250000+0+250000)/(3)}`

or

`\sigma=408.24`

and, after the raise

the average = ( $3,600 + $4,100 + $4,600 ) / 3 = $4,100

now,

the standard deviation ,

`\sigma=\sqrt{((4,100-3600)^2+(4,100-4100)^2+(4,100-4600)^2)/(3)}`

or

`\sigma=\sqrt{(250000+0+250000)/(3)}`

or

`\sigma=408.24`

therefore, The standard deviation would stay the same