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Measure of variability is needed to indicate the degree to which individual observation are clustered about or deviate from that average value. In general, how different the observation is from each other.
Types of measure of variability
1.Range
Range is the difference between the largest and the smallest observations.
Limitations of the range as measure o variability in data
a) It ignores almost all the observations in the distribution and is calculated from the extreme values.
b) It is influenced by the sample size. The more values / observations you have, the further apart the smallest and the largest of those values are likely to be.
c) The inter quartile range is obtained by discarding the upper and the lower 25% of the distribution and taking the range of what remains . The aim is to reduce the problem of the range being heavily dependent on extreme scores which may not be representative of the entire data .For example determine the range of the following data.
6, 7, 8,4,6,10,15,
Range = 15 - 4 =11
Range = 11
2. Variance
Sample variance is denoted by the symbol S2 while population variance is denoted by a2 Population variance is equal to the sum of squared deviation from the mean divided by the number of observations in the population N.
3. Standard deviation
Variance is the squared units which are awkward to interpreted and report. Standard deviation (denoted a which is the square root of variance is therefore more commonly used. Standard deviation is basically a measure of the average of the deviation of each score from the mean.
NatalieR answered the question on June 6, 2022 at 11:57
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