Can someone please tell me how to calculate the standard deviation of the following values?
0.985 0.985 1.005 1.455 1.035
And please for the following numbers too
1.47 1.52 1.50 1.45 1.39
To calculate the standard deviation of a set of values, follow these steps:
1. Calculate the mean (average) of the values.
- Add up all the values and divide the sum by the number of values.
For the first set of values:
Average = (0.985 + 0.985 + 1.005 + 1.455 + 1.035) / 5 = 1.09
For the second set of values:
Average = (1.47 + 1.52 + 1.50 + 1.45 + 1.39) / 5 = 1.466
2. Calculate the difference between each value and the mean.
- Subtract the mean from each value.
For the first set of values:
0.985 - 1.09 = -0.105
0.985 - 1.09 = -0.105
1.005 - 1.09 = -0.085
1.455 - 1.09 = 0.365
1.035 - 1.09 = -0.055
For the second set of values:
1.47 - 1.466 = 0.004
1.52 - 1.466 = 0.054
1.50 - 1.466 = 0.034
1.45 - 1.466 = -0.016
1.39 - 1.466 = -0.076
3. Square each difference.
- Multiply each difference by itself.
For the first set of values:
(-0.105)^2 = 0.011025
(-0.105)^2 = 0.011025
(-0.085)^2 = 0.007225
(0.365)^2 = 0.133225
(-0.055)^2 = 0.003025
For the second set of values:
(0.004)^2 = 0.000016
(0.054)^2 = 0.002916
(0.034)^2 = 0.001156
(-0.016)^2 = 0.000256
(-0.076)^2 = 0.005776
4. Calculate the average of the squared differences.
- Add up all the squared differences and divide the sum by the number of values.
For the first set of values:
Average of squared differences = (0.011025 + 0.011025 + 0.007225 + 0.133225 + 0.003025) / 5 = 0.0337
For the second set of values:
Average of squared differences = (0.000016 + 0.002916 + 0.001156 + 0.000256 + 0.005776) / 5 = 0.001024
5. Calculate the square root of the average of the squared differences.
- Take the square root of the result from step 4.
For the first set of values:
Standard Deviation = Square root of 0.0337 ≈ 0.183
For the second set of values:
Standard Deviation = Square root of 0.001024 ≈ 0.032