Descriptive Statistics

What are measures of central tendency?

A single value that summarises a set of data by identifying the typical value of the data set, also known as an average

What are the 3 measures of central tendency?

• Mode

• Median

• Mean

What is ‘mode’?

The most frequent score in a quantitative data set. If there are two modes, the data is bi-modal, and if there are more than two modes, the data set is multimodal

(Mode) AO3 - Strengths

• The mode is not distorted by extreme scores called outliers

• The mode is helpful for discrete numbers eg it can make more sense to say the average family has 1 children not 1.89 children

• Giving the modal group is the only way of giving the average data in categories (eg average pet choice)

(Mode) AO3 - Limitations

• There can be no modes if every value is different or multiple modes, this is especially likely in small data sets. This means in some cases, the mode does not give an exact average value

• The mode does not include all of the values in its calculation, so it is not as sensitive as the mean measure of central tendency

What is ‘median’?

The value in the central position of a data set. The median is calculated by ordering the values from lowest to highest and selecting the value in the middle. If there are an even number of data points, then the median is the halfway point between the two centre values

(Median) AO3 - Strengths

• As the median is the central value, its calculation is not affected by extreme outlier scores

• The median is very easy to calculate

(Median) AO3 - Limitations

• The median score does not include all of the values in its calculation, so it is not as sensitive as the mean measure of central tendency

• If there are an even number of data points, unlike the mode, the ‘typical’ value will be a number that is not one of the recorded values

What is ‘mean’?

The arithmetic/mathematical average, calculated by adding all the values then dividing by the number of values

(Mean) AO3 - Strengths

• All raw data points are used (represented) in calculating the mean. This means the mean is the most sensitive measure of central tendency

(Mean) AO3 - Limitations

• Due to the sensitivity of the mean, the mean is distorted by extremely high or low values (outliers)

What is ‘the range’?

The range is the difference between a data sets highest and lowest values. To calculate the range subtract the smallest value in the data set from the largest (adding one to this figure is also a correct way of stating the range)

(Range) AO3 - Strengths

• The range is easy to calculate, especially compared to the alternative measure of dispersion, the standard deviation

What does measures of dispersion mean?

A single value that summarises the spread of a set of data

What are the 2 measures of dispersion?

• The range

• Standard deviation

(Range) AO3 - Limitations

• Extreme scores easily distort the value

• The range does not show if the scores are clustered around the mean or more evenly spread out

What is ‘standard deviation’?

The standard deviation is a complex calculation using all data points that produces a single value. The smaller the standard deviation more clustered (less spread out/variable) the values are around the mean

(Standard Deviation) AO3 - Strengths

• The standard deviation includes all values in its calculation, making it more sensitive than the range

• The standard deviation provides information about the spread of scores

(Standard Deviation) AO3 - Limitations

• Extreme scores also distort the standard deviation

• The standard deviation is significantly more difficult to calculate than the range