Question

Find the mean and standard deviation of the following list of quiz scores: 79, 88, 65, 90. Round the standard deviation to two decimal places.

Answer 1

mean = 80.5

standard deviation = 9.86

Given:

79, 88, 65, 90

To find the mean, we will use the following formula:

`\mu=(\Sigma x)/(N)`

Where:

μ = mean

Σx = sum of all data points

N = number of data points

Using the given data, we know that:

Σx = 79+88+65+90

N = 4

`\mu=(79+88+65+90)/(4)`
`\mu=80.5`

Next, finding the standard deviation will be easier if we find the variance first. To find the variance, we will use the following formula:

`\sigma^2=(\Sigma(x-\mu)^2)/(N)`

And using the same data as earlier,

`\sigma^2=97.25`

And then, to find the standard deviation, we are just going to get the square root of the variance

`\sigma=\sqrt[]{\sigma^2}`
`\sigma=\sqrt[]{97.25^{}}`
`\sigma=9.86`

Answer:

mean = 80.5

standard deviation = 9.86