Measures of Central Tendency (1)

Measures of central tendency

• Measures of central tendency describe the central or typical value of a data set

• Measures of central tendency are used to summarise large amounts of data into typical mid-point scores

• There are three measures of central tendency

  • the mean

  • the median

  • the mode

The Mean

• The mean calculates the average score of a data set 

• The mean indicates what a researcher would expect to find (as the average score) if they were to replicate the procedure of a given study

• 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

Example of the mean

• To calculate the mean of 4, 6, 7, 9 add up the values and then divide this total by the number of values

  • 4 + 6 + 7 + 9 = 26

  • 26 ÷ 4 = 6.5

  • mean = 6.5

Evaluation of the mean - Strengths

• The mean is the most sensitive measure of central tendency as it takes all scores in the data set into account

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

  • This means that it is the most reliable measure of central tendency  

Evaluation of the mean - Limitations

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

  • This means that it would not be a suitable measure for some data sets

• The mean score may not be represented in the data set itself

  • In the example provided above, the mean is 6.5 which does not appear in the original data set itself

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),

Example of the median

• For an odd number of values

  • To calculate the median of 20, 43, 56, 78, 92, 67, 48 take the halfway point as the data set has an odd number of scores (7)

  • 20, 43, 56, 78, 92, 67, 48 is ordered into 20, 43, 48, 56, 67,78, 92

  • Median = 56 as this is the value at the halfway point in the set

• For an even number of values, there are two values at the halfway point

  • E.g. 15, 16, 18, 19, 22, 24

  • The halfway point is between 18 and 19

  • Add the two middle values (18 + 19 = 37)

  • Divide the total by 2 (37 divided by 2 = 18.5)

  • Thus, the median = 18.5

Evaluation of the median - Strengths

• The median is not affected by extreme scores

  • This means that it can be used on data sets with anomalous scores

• The median is the best measure of central tendency when dealing with qualitative data where ranking of categories or themes is used instead of measurement or counting

Evaluation of the median - Limitations

• The median does not necessarily represent a typical average as it does not include all of the data in its calculation

  • It does not account for extreme scores making it less reliablethan the mean

  • Arranging the data in ascending or descending order is time-consuming

    • This makes the median more problematic in dealing with large data sets

Mode

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

  • Mode means most often

• The mode identifies the most common score(s) in a data set

• Some data sets may have:

  • no mode

  • two modes (known as bi-modal)

  • more than two modes (known as multi-modal)

• The mode is used when the researcher cannot use the mean or the median e.g.

  • a researcher wishes to measure how many times litter is dropped in a naturalistic observation

    • The only measure of central tendency applicable to this research is the mode as it measures frequency rather than average score or middle value

Example of the mode

• To calculate the mode of 3, 3, 3, 4, 4, 5, 6, 6, 6, 6, 7, 8 count the number of times each score appears in the data set

  • The most frequently occurring number is 6 

  • Thus, the mode = 6 

Evaluation of the mode - Strengths

• The mode is not affected by extreme values

• The mode is often useful for the analysis of qualitative data

  • This type of data may require frequencies of theme to beanalysed 

Evaluation of the mode - Limitations

• A data set may include two modes or more which blurs the meaningof the data, making it difficult for the researcher to form conclusions

  • This means that the mode is the least reliable of the measures of central tendency

• The mode is likely to be of little use on small data sets as it may provide an unrepresentative central measure e.g.

  • A data set may include a mode of 73 when in fact the average score in that set is 55

  • This means that the mode may lack validity