Biology, images, analysis, design...
|"It has long been an axiom of mine that the little things are infinitely the most important" |
Variance and standard deviation
Calculating variance from individual observations
These are the data on the weights of thirty cattle that we gave in the More Information page on Measures of location.
The sample standard deviation (s) is then the square root of the variance.
Standard deviation (s) = √1713.3 = 41.4
Calculating variance from a frequency distribution
Let us assume you have the following observations of bird weight (in grams), which have been divided into class intervals, but you not know their individual values, nor their mean.
Lacking their mean, we can estimate it by multiplying the mid-point of each class by the number of observations it contains.
Now we can work out the deviation of each mid-class from the sample mean. Then multiply the square of this deviation by the number of observations it refers to.
s2 = 6474.2 / 45, or 143.9
Calculating the corrected standard deviation for a small sample
Let's take an example of packed cell volume values of five lambs:
The (uncorrected) sample standard deviation (s) is then:
s = √ 7.7 = 2.775
The corrected standard deviation is then given by:
scorr. = Cn × s = 1.064 × 2.775 = 2.953
Calculating within-subject standard deviation
Let's take an example of two repeated measurements of packed cell volume.
Hence, assuming the observations are normally distributed: