A measure of dispersion is a method of measuring the degree by which numerical data or values tend to spread from or cluster about central point of average.
The most common measures of dispersion are the following:
- The range
- The Quartile Deviation
- The Standard Deviation
Range
Range is the difference between the smallest and largest number in a set of data.
Formula for range is divided into 2, which is:
- For ungrouped data:
R=H-L
- For group data:
R=UB-LB
The Quartile Deviation
It is based on the lower quartile (Q1) and the upper quartile (Q3). The difference of Q3 -Q1 is called the Inter quartile range. The defference of Q3-Q1 divided by 2 is called semi-interquartile range or the quartile deviation.
Formula for quartile deviation is:
Quartile Deviation=Q3-Q1/2
Standard Deviation
It is a number used to tell how measurements for a group are spread put from the average(mean), or expected value. A low standard deviation means that most of the numbers are very close to the average while high standard deviation means that the numbers are spread out.
Formula for standard deviation:
For a good explanation regarding Measure of Dispersion:
- For group data:
The Quartile Deviation
It is based on the lower quartile (Q1) and the upper quartile (Q3). The difference of Q3 -Q1 is called the Inter quartile range. The defference of Q3-Q1 divided by 2 is called semi-interquartile range or the quartile deviation.
Formula for quartile deviation is:
Standard Deviation
It is a number used to tell how measurements for a group are spread put from the average(mean), or expected value. A low standard deviation means that most of the numbers are very close to the average while high standard deviation means that the numbers are spread out.
Formula for standard deviation:
