Descriptive Statistics: Understanding & Calculating (AQA GCSE Psychology): Revision Note

Mean

• The mean calculates the average score of a data set

• The mean is calculated using the total score of all the values in the data set divided by the number of values in that set, e.g.:

  • To calculate the mean of 4, 6, 7, 9: 4 + 6 + 7 + 9 = 26; 26 ÷ 4 = 6.5; mean = 6.5

• Advantages of using the mean

  • It is the most sensitive measure of central tendency, as it is the only average that takes every score in the data set into account

  • It is more likely than other measures of central tendency to provide a representative score

• Disadvantages of using the mean

  • It is sensitive to extreme scores (outliers), so it can only be used meaningfully when the scores are reasonably close together

  • The mean score may not be represented in the data set itself: in the example above, the mean is 6.5, which does not appear in the original data set

Median

• The median calculates the middle value of a data set (the positional average)

• The data must first be arranged into numerical order, lowest to highest

• If there is an odd number of scores, there is a single middle value

  • This is the median, e.g. for 20, 43, 56, 78, 92, 67, 48 (7 scores):

    • Ordered: 20, 43, 48, 56, 67, 78, 92

    • The middle (4th) value is 56, so the median = 56

• If there is an even number of scores, there are two middle values - add them together and divide by 2

  • This is the same as finding the mean of the middle two values, e.g. for 8, 8, 9, 9, 9, 10, 12, 13, 15, 16 (10 scores):

  • The two middle values are 9 and 10

  • (9 + 10) ÷ 2 = 9.5, so the median = 9.5

• Advantages of using the median

  • It is not affected by extreme scores

  • It is easy to calculate

• Disadvantages of using the median 

  • It does not use the actual value of every score in the data set, therefore it is not representative of the whole data set

  • It is impractical to use on large data sets, as the values must first be sorted into order, which becomes time-consuming as the data set grows

Mode

• The mode calculates the most frequently occurring score in a data set i.e. mode means most often

• The mode is used when the mean and median can't meaningfully be calculated

  • e.g. with categorical (nominal) data, such as favourite colour, where scores have no numerical order

• To find the mode of 3, 3, 3, 4, 4, 5, 6, 6, 6, 6, 7, 8: count how often each score appears

  • 6 appears most often (four times), so the mode = 6

• Advantages of using the mode

  • It is less likely to be affected by extreme scores

  • It is useful for analysing qualitative data, where frequencies of a theme need to be counted

• Disadvantages of using the mode

  • A data set may include two modes (bimodal) or more (multimodal) which blurs the meaning of the data

  • It does not use the actual value of every score in the data set, therefore it is not representative of the whole data set

Calculating the mode, median and mean

Range

• The range is a measure of dispersion

  • It describes the difference between the lowest and highest scores in a data set

• To calculate the range, subtract the lowest value from the highest value, e.g. for 4, 4, 6, 7, 9, 9:

  • 9 − 4 = 5

  • The range = 5

• Advantages of using the range

  • It provides a quick, broad overview of the data

  • It is easy to calculate

• Disadvantages of using the range 

  • It only takes into account the two most extreme scores, so a single unusually high or low score can distort it, making it unrepresentative of the data set as a whole

  • It gives no information about the distribution of scores between the highest and lowest values