Research Methods RE: Measures of Dispersion

Measures of central tendency give an idea of a typical value
Measures of dispersion describe the spread of data around the central value
Measures of central tendency should include a measure of dispersion of the data

Three measures of dispersion

• Range
• Semi-interquartile Range
• Standard Deviation

Range
Simplest measure of dispersion and is calculated by subtracting the lowest score in the data set from the highest score.
e.g. 'Days of work because of sickness'
3,5,6,6,6,8,9
9 - 3 = 6

The range is mostly used as a measure of dispersion with the mode and median

Advantages:

• Easy to calculate
• Takes into consideration extreme score

Disadvantages:

• Only using two scores in the data set and ignoring the rest
• The extreme scores could distort the range

Semi-interquartile Range
This measure of dispersion is normally used with the median as the measure of central tendency. The range can also be used with the median.

The Semi-interquartile Range is a measure of the spread of the middle 50% of the data, i.e. 25% of data below the median and 25% above the median.
Having set the data out in order. It ignored the lowest quarter and highest quarter of the data set.
The whole data set if set out on a scale may be represented as a Box and Whisker plot.

Advantages:

• The Semi-interquartile Range is less distorted be extreme scores than the range

Disadvantages:

• It only relates to 50% of the data set, ignoring the rest of the data set
• It can be laborious and time consuming to calculate by hand

Standard Deviation
This measure of dispersion is normally used with the mean as the measure of central tendency.
The Standard Deviation (SD) tells the mean distance of the scores in the data set from the mean.
A large SD describes scores that are widely spread out above and below the mean, suggesting the mean is not representative of the data set.
If the SD is small than the mean more closely represents the scores in the data set.

Formula:
1. Calculate the mean, x with a line over it, x-bar
2.Set up a table, column 1 is x, write down each value of the data set, then subtract the mean from each value in column 1 and write answer in column 2
3. Multiply each figure in column 2 by itself and write in column 3 (Squaring)
4. Add all the numbers in column 3 then divide by the number of scores in the data set (n) then square root this figure to get the SD

Advantages:

• SD is the most sensitive measure of dispersion as it is derived by using every score in the data set ans is not very distorted by extreme scores. The SD is closely related to the mean and is the best measure of dispersion to use when the mean is being used as the measure of central tendency

Disadvantages:

• Laborious to calculate but calculators make so it easy!