Measures of central tendency and dispersion

Measures of central tendency

• 'Averages' which give us information about the most typical values in a set of data. There are three of these to consider: Mean, median, and mode

Measures of central tendency: Mean

• Calculated by adding up all the scores or values in a data set and dividing this figure by the total number of scores there are

Measures of central tendency: Mean strengths

• The most sensitive of the measures of central tendency as it includes all of the scores/values in the data set within the calculation. It is more representative of the data as a whole

Measures of central tendency: Mean weaknesses

• It is easily distorted by extreme values

Measures of central tendency: Median

• The middle value in a data set when scores are arranged from lowest to highest. In a odd number of scores, it is easily identified. In an even number of scores, it is halfway between the two middle scores

Measures of central tendency: Median strengths

• Extreme scores do not affect it. Also easy to calculate (once the numbers have been arranged in order)

Measures of central tendency: Median weaknesses

• Less sensitive as the actual values of lower and higher numbers are ignored and extreme values may be important

Measures of central tendency: Mode

• Most frequently occurring score/value within a data set. In some data sets there may be two of these or none if all the scores are different

Measures of central tendency: Mode strengths

• Very easy to calculate

Measures of central tendency: Mode weaknesses

• Not practical for large number categories. Also not representative of the whole data set

Measures of dispersion

• Based on the spread of scores. That is, how far scores vary and differ from one another. This includes the range and standard deviation

Measures of dispersion: Range

• Taking the lowest value from the highest value and (usually) adding 1. Adding 1 is a mathematical correction that allows for the fact that raw scores are often rounded up (or down) when they are recorded within research

Measures of dispersion: Range strengths

• Easy to calculate

Measures of dispersion: Range weaknesses

• Only takes into account the two most extreme values, and this may be unrepresentative of the data set as a whole. Also influenced by outliers. It also does not indicate whether most numbers are closely grouped around the mean or spread out

Measures of dispersion: Standard deviation

• A single value that tells us how far scores deviate (move away) from the mean

Measures of dispersion: Standard deviation (Large)

• The larger this is, the greater the dispersion or spread within a set of data. If we are talking about a particular condition within an experiment, a large version of this suggests that not all participants were affected by the IV in the same way- the data is widely spread. It may be that there a few anomalous results

Measures of dispersion: Standard deviation (Low)

• A low version of this reflects the fact that the data is tightly clustered around the mean, implying all participants responded in a similar way

Measures of dispersion: Standard deviation strengths

• Much more precise measure of dispersion than the range as it includes all values within the final calculation

Measures of dispersion: Standard deviation weaknesses

• Like the mean, it can be distorted by a single extreme value. Also, extreme values may not be revealed, unlike with the range