What are the variance and standard deviation of {18, -9, -57, 30, 18, 5, 700, 7, 2, 1}?
2 Answers
Assuming we are dealing with the entire population and not just a sample:
Variance
Standard Deviation
Explanation:
Most scientific calculators or spreadsheets will allow you to determine these values directly.
If you need to do it in a more methodical way:
- Determine the sum of the given data values.
- Calculate the mean by dividing the sum by the number of data entries.
- For each data value calculate its deviation from the mean by subtracting the data value from the mean.
- For each data value's deviation from the mean calculate the squared deviation from the mean by squaring the deviation.
- Determine the sum of the squared deviations
- Divide the sum of the squared deviations by the number of original data values to get the population variance
- Determine the square root of the population variance to get the population standard deviation
If you want the sample variance and sample standard deviation:
in step 6. divide by 1 less than the number of original data values.
Here it is as a detailed spreadsheet image:
Note: I would normally simply used the functions
and
instead of all these details
Variance = 44383.45
Standard deviation
Explanation:
The mean is given by
The variance is given by
The standard deviation is given by