# Measures of Dispersion (Range and Standard Deviation)

Measures of Dispersion: Standard Deviation:

In order to summarise a set of scores, a measure of central tendency is important, but on its own it is not enough. A measure of central tendency (such as the mean) doesn’t tell us a great deal about the ‘spread’ of scores in a data set (i.e. is the data made up of numbers that are similar or different?)

Consider the following table of scores:

### SET A

35 48 49 34 42 40

### SET B

3 25 47 50 79 90

In this set of data it can be seen that the scores in data set A are a lot more similar than the scores in data set B. The mean of data set A is 46. 46 can be considered to be a good representation of this data (the mean score is not too dis-similar to each individual score in the data set).

The mean of data set B is 49. This mean score (49) doesn’t appear to best represent all scores in data set B. For example, the number ‘3’ makes up part of data set B, this score is not similar in the slightest to the much higher mean score of ’49.’

Due to the possibility that (on occasion) measures of central tendency won’t be the best way for a number to represent a whole data set, it is important to present a measure of dispersion alongside a measure of central tendency. This allows those reading the data to understand how similar or dissimilar numbers in a data set are to each other.

Revision Note: In your exam, you will not be asked to calculate the Standard Deviation of a set of scores. You may however be asked to interpret a standard deviation value (explain to the examiner what the measure means).

Standard Deviation (SD:

This measures the average deviation (difference) of each score from the mean. Every score is involved in the calculation and it gives an indication of how far the average participant deviates from the mean. A small SD would indicate that most scores cluster around the mean score (similar scores) and so participants in that group performed similarly, whereas, a large SD would suggest that there is a greater variance (or variety) in the scores and that the mean is not representative.

Exam Tip: Be careful when reading tables that have a SD. The smaller SD does not mean that that group of participants scored less than the other group – it means that their scores were more closely clustered around the mean and didn’t vary as much.

low standard deviation score indicates that the data in the set are similar (all around the same value – like in the data set A example above). A low standard deviation suggests that, in the most part, the mean (measure of central tendency) is a good representation of the whole data set.

A high standard deviation score indicates that the data/some of the data in the set are very different to each other (not all clustered around the same value – like the data set B example above). A high standard deviation suggests that, in the most part, the mean (measure of central tendency)is not a goof representation of the whole data set.

Evaluation of using Standard Deviation as a Measure of Dispersion (AO3):

Advantage:

(1) It is the most precise measure of dispersion. For example, the standard deviation considers all available scores in the data set, unlike the range. This is a strength because it means that the standard deviation is the most representative way of understating a set of day as it takes all scores into consideration.

Disadvantage

(1) It requires the mean to be the measure of central tendency and therefore, it can only be used with interval data, because ordinal and nominal data does not have a mean. This is a weakness as the standard deviation does not cover all data types within its use and therefore is limited with regards to its use.

(2) It is also quite time consuming to calculate. In order to calculate the standard deviation use individual data score needs to be compared to the mean in order to calculate the standard deviation. In a set of data that has many scores this would take a great deal of time to do. This is a weakness as it would make data analysis very tedious and difficult.

Measures of Dispersion – The Range:

Due to Standard Deviation being criticised for the complex nation in which it is calculates, the most straightforward measure of dispersion to calculate would be the Range. This measure of dispersion is calculated by simply subtracting the lowest score in the data set from the highest score, the result of this calculation is the range.

Advantage:

(1) A strength of the range as a measure of dispersion is that it is quick and easy to calculate. As stated above, the range is calculated by subtracting the smallest value in the data set from the largest value in the data set. This is a strength as this speeds up data analysis allowing psychologists and researchers to draw conclusions about their research at a faster pace. It also means that researchers can spend more time interpretating and drawing inferences from the data as oppose to calculating and analysing.

Disadvantage:

(1) The range is vulnerable to extreme score. For example, say the last score in set A wasn’t 40 but 134, this would bump the range for set A up to 100, giving a misleading impression of the real dispersion of scores in set A. This is a weakness as it can be argued that the range is not always a representative description of the spread of a set of data.