Question

If the variance of the ages of the people who attended a rock concert is 38, what is the standard deviation of the ages? Round your answer to two decimal places

Answer 1

`\sigma=6.16`

Explanation:

By definition, the variance V of a population is defined as:

`V = \sigma^2`

Where
`\sigma` is the standard deviation

We know that
`V = 38`, then we can solve the equation for the standard deviation
`\sigma`

`38 = \sigma^2`

`\sigma^2=38`

`\sigma=√(38)`

`\sigma=6.16`

Finally the standard deviation is:
`\sigma=6.16`

Answer 2

The standard deviation of the age is 6.16

Explanation:

* Lets talk about the variance and the standard deviation

- The variance is the measure of how much values in a set of data are

likely to differ from the mean value of the same data

- The steps to find the variance are:

1- Find the mean of the data

2- Subtract the mean from each value and square the answer

3- Add all of these squared answer and divide the sum by the number

of the values

- The answer of the step 3 is The variance (σ²)

- The standard deviation (σ) is the square root of the variance

* Now lets solve the problem

∵ The variance of the ages of the people who attended a rock

concert is 38

∴ σ² = 38

∵ The standard deviation is the square root of the variance

∴ σ = √38 = 6.16

* The standard deviation of the age is 6.16