Question

Calculate the standard deviation of the following data. 3, 4, 5, 6, 2, 3, 12, 79, 5

Answer 1

24.8

Explanation:

Answer 2

The answer to this is 23.42 (For population, SD)

The data given as a whole is called UNGROUPED data. The standard deviation can be computed with the formula:


`\sqrt{\frac{\sum(x_i-\bar{x})^2}{n}}`

To do this, you need to first figure out the following:

Mean (
`\bar{X}`) =?
The sum of
`\sum(x_i-\bar{X})^(2)` =?

You need to write down your data in a table, but before you can do this, you need to first find out what the mean is and you can do this by adding up all the data and dividing it by the number of observations:


`\bar{X} = (sum of all data)/(number of observations)`

`\bar{X} = (3+4+5+6+2+3+12+79+5)/(9) = (119)/(9)= 13.22`

So we subtract the mean from each data to fill in the second column. I'll use the first raw data to make the first row as an example here:

`(x-\bar{X}= 3-13.22=-10.22)`

For the third column, you just need get the square of the second column.

`(x_i-\bar{X})^(2) =(-10.22)^(2)= 104.4484`

For this table, let x be raw data and X be
`\bar{X}`:

x | (x-X) | (x-X)²
3 | -10.22 | 104.4484
| |
4 | - 9.22 | 85.0084
| |
5 | - 8.22 | 67.5684
| |
6 | - 7.22 | 52.1284
| |
2 | - 11.22 | 125.8884
| |
3 | -10.22 | 104.4484
| |
12 | - 1.22 | 1.4884
| |
79 | 65.78 | 4327.0084
| |
5 | - 8.22 | 67.5684

REMEMBER: The Σ means "the sum of" to get Σ(x-X)² Add the values in the third column to get the sum of (x-X)² and you will get 4,935.5556

Now all you have to do is input it into your equation:


`sd=\sqrt{\frac{\sum(x_i-\bar{x})^2}{n}}`

`\sqrt{(4935.5556)/(9)}`

`√(548.39506666)`

`23.42`

The standard deviation is 23.42