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

Answer:

mean = 80.5

standard deviation = 9.86

Given:

79, 88, 65, 90

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

$\mu=\frac{\Sigma x}{N}$

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=\frac{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:

$\sigma^2=\frac{\Sigma(x-\mu)^2}{N}$

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