Find the standard deviation of the following set of data:
| 5.57 | 5.40 | 8.08 | 6.93 | 2.05 |
| 5.51 | 3.31 | 8.74 | 6.00 | 6.59 |
| 5.67 | 1.97 | 3.05 | 4.27 | 3.61 |
| 5.09 | 5.43 | 6.59 | 6.11 | 5.70 |
Put all the data in column A from A1 to A20. From the Tools menu we choose Data Analysis. If Data Analysis is not there, choose Add-Ins from the Tools menu and check the Analysis ToolPak option. Data Analysis will then appear under the Tools menu.
Here is the output:
| Column1 | |
| Mean | 5.2835 |
| Standard Error | 0.403157 |
| Median | 5.54 |
| Mode | 6.59 |
| Standard Deviation | 1.802975 |
| Sample Variance | 3.250719 |
| Kurtosis | -0.14377 |
| Skewness | -0.21511 |
| Range | 6.77 |
| Minimum | 1.97 |
| Maximum | 8.74 |
| Sum | 105.67 |
| Count | 20 |
You'll notice the output contains most of the statistics that are commonly used such as the mean, median and standard deviation. A couple that warrant a word or two are the skewness and kurtosis.
The skewness describes the shape of the data. If the value is roughly zero, then the data is symmetric. If the value is positive, then the data is skewed right - indicating that most of the data is to the left. (Expecting right, weren't you?) Similarly, if the value is negative, then the data is skewed left - indicating that most of the data is to the right.
The kurtosis indicates the peakedness of the data. A value of around zero indicates a perfect bell curve. The more negative the value become, the flatter the data is. The more positive the value become, the more peaked the data is.
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