Measures of central tendency & dispersion

What are descriptive statistics

The use of graphs, tables, and summary statistics to identify trends and analyse sets of data. They are measures of central tendency

What are measures of central tendency

‘Averages’ which give us information about the most typical values in a set of data. Includes: mean, median, mode

Pros and cons of the mean

Pros: the most sensitive of the measures of central tendency as it includes all of the scores/values in the data set in the calculation - means it is more representative of the data as a whole

Cons: easily distorted by extreme values

Pros and cons of the median

Pros: extreme scores do not affect it and easy to calculate

Cons: less sensitive than the mean as the actual values of lower and higher numbers are ignored and extreme values may be important

Pros and cons of the mode

Pros: easy to calculate

Cons: very crude measure, not representative of whole data set, if there are several modes it is not very useful

What are measures of dispersion

Based on the spread of scores - how far scores vary and differ from one another. Includes: range, standard deviation

Pros and cons of the range

Pros: easy to calculate

Cons: only takes into account the two most extreme values therefore unrepresentative of the data set as a whole, influenced by outliers, doesn’t indicate whether most numbers are closely grouped around the mean or spread out

What is standard deviation and what does it show

A single value that tells us how far scores deviate from the mean. The larger the standard deviation, the greater the dispersion within a set of data. If we are talking about a particular condition within an experiment, a large SD suggests that not all participants were affected by the IV in the same way because the data is widely spread (may be a few anomalous results). A low SD implies that all participants responded in a failry similar way

Pros and cons of standard deviation

Pros: much more precise measure of dispersion than the range as it includes all values in the final calculation

Cons: can be distorted by a single extreme value, extreme values may not be revealed unlike with the range