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

Descriptive statistics

• In psychology, descriptive statistics are used to summarise large amounts of data so that patterns and trends can be identified

• Rather than showing every raw score, researchers use measures such as the mean, median and mode to show what is typical of a data set

• These are known as measures of central tendency because they describe the average or ‘centre’ of a set of scores

Mean

• The mean calculates the average score of a data set 

  • It is calculated by adding all the scores together and dividing the total by the number of scores

• For example:

  • Scores in a data set = 4, 6, 7, 9

  • 4 + 6 + 7 + 9 = 26

  • 26 ÷ 4 = 6.5, so the mean is 6.5

Evaluation of the mean

Strengths

• It is the most sensitive measure of central tendency, as it uses all scores in the data set

• The mean provides a representative summary when there are no extreme scores

Weaknesses

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

• 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 has to be arranged into numerical order first (with the lowest score at the beginning of the list)

  • If there is an even number of scores, the median is the halfway point between the two middle values

• For example:

  • Scores in a data set: 20, 43, 56, 78, 92, 67, 48

  • The median is 78

• Another example:

  • Scores in a data set: 20, 43, 48, 56, 78, 92, 67, 48

  • As there is an even set of scores, the two middle values are added together and divided by two

  • (56 + 78) ÷ 2 = 67, so the median is 67

Evaluation of the median

Strengths

• The median is not affected by extreme scores

• It is simple to calculate for small data sets

Weaknesses

• The median ignores most of the data, so it may not be truly representative of the data set

• The median is not suitable for large data sets

Mode

• The mode is the most frequently occurring score in a data set

  • Some data sets have no mode; others may be bimodal (two modes) or multimodal (more than two)

• For example:

  • Scores in a data set: 3, 3, 3, 4, 4, 5, 6, 6, 6, 6, 7, 8

  • Mode = 6, as it occurs most frequently (4 times)

Evaluation of the mode

Strengths

• The mode is not affected by extreme scores

• It is useful for describing categorical or qualitative data

Weaknesses

• The mode can be unrepresentative of the data set, as it doesn't take all of the values into account

• Multiple modes can make interpretation unclear

Range

• The range is a measure of dispersion, showing how spread out the scores are and how much they vary from the mean

  • It is calculated by subtracting the lowest score from the highest score

• For example

  • Scores in a data set: 4, 4, 6, 7, 9, 9

  • 9 − 4 = 5, so the range is 5

Evaluation of the range

Strengths

• The range is quick and easy to calculate

• It gives a clear indication of data spread, which tells the researcher how consistent the scores are

Weaknesses

• The range can be unrepresentative of the data set, as it doesn't take all of the values into account

• The range only considers the two extreme scores, so it can be distorted by outliers