Standard dev. and mean?

Question

how do you calculate the standard deviation and the mean of 190 and 225

could you explain it step by step? thanks

Answer 1

You have two entries - 190 and 225
∑ x = 415
μ = 415 / 2 = 207.5

Now there are two definitions for standard deviation.
σ_n = sqrt [(∑ x^2 - n*μ^2) / n]
and
σ_n-1 = sqrt [(∑ x^2 - n*μ^2) / (n-1) ]

σ_n = 17.5
σ_n-1 = 24.749

When n is large, there isn't really a big difference between the two std dev values. In this case, there is a big difference.

Answer 2

The mean is just the arithmetic mean or "average." It's the sum of the numbers, divided by the quantity of values that were added. We have two numbers, so the mean is (190 + 225) / 2 = 415/2 = 207.5. When we only have two data points, the standard deviation is a special case. It is just equal to the difference between each number and the mean, or half the difference between the two numbers, which are identical values. 207.5 - 190 = 225 - 207.5 = (225 - 190) / 2 = 35/2 = 17.5. Normally, you need to sum up the squares of the differences between each number and the average and take the square root of the average of those values.

Answer 3

1st lets find the mean or also known as the average
(190 + 225) / 2 = 207.5
we divide by the number of data there are

now this comes the tricky part
deviation = (difference between data and mean)
data mean deviation squared deviation
190 207.5 17.5 306.25
225 207.5 17.5 206.25


add the squared deviation = 612.5

standard deviation = square root of the (sum of the squared deviation divided by (the total number of data) minus 1

standard deviation = square root (612.5/1) = 24.749