Question

Calculate the standard deviation of the data set below. (7, 9, 10, 11, 13) The standard deviation is 4. The standard deviation is 2. The standard deviation is 10.

Answer 1

The standard deviation is 2.

Explanation:

The standard deviation of 7, 9, 10, 11, 13

We first calculate the mean

Mean = (7+9+10+11+13)/5

= 10

Then we find the deviation of the values from the mean,

= (7-10), (9-10), (10-10), (11-10), (13-10)

= -3, -1, 0, 1, 3

The we get the square of deviations;

= (-3)², (-1)², 0², 1², 3²

= 9, 1, 0, 1, 9

We then get the sum of the square of deviations

= 9 + 1 + 0 + 1 + 9

= 20

Standard deviation = √(sum of the square of deviations/(x-1))

= √(20/(5-1)

= √5

= 2.2

Therefore; The standard deviation is 2

Answer 2

"The standard deviation is 2"

Explanation:

To get Standard Deviation (SD), we follow the steps shown below:

1. We need to find the difference of each number from the mean and then square it.
2. Then take the sum of all of these values.
3. Then divide by the number of numbers.
4. Then take square root of that.

The mean is summing up all the numbers and dividing by the number of numbers. Hence, mean is
`(7+9+10+11+13)/(5)=10`

Now,
`(7-10)^2 + (9-10)^2 + (10-10)^2 + (11-10)^2  +(13-10)^2\\=9+1+0+1+9\\=20`

Then,
`(20)/(5)=4`

Next,
`√(4) \\=2`

So, the standard deviation is 2