Measures of Central Tendency Measures of Central Tendency

Measures of Central Tendency

Measures of Central Tendency DEF: Those measurements that indicate the central values of a data set (the averages) How many are there? 3 What are they called? Mean – Median - Mode

Definitions of the three measures of central tendency Definition Mean The value resulting from adding all the numbers up in a data set, and dividing by the number of values in the data set. Median The central number in a data set that has been placed in chronological order. A mean average of both central values is taken when the sample has an equal number of values. Mode The most common occurring number in a data set

Measures of Central Tendency • How do you work out the mean? One adds up all the values in the data set and divides by the number of values What is the mean for this data set? 34 56 57 89 102 122 583/ 7 = 83. 2 123

Measures of Central Tendency • What is the median of this data set 14 14 15 16 16 16 17 17 18 19 20 22 The median is 16+17/2 = 16. 5 • What is the mode of this data set 14 14 15 16 16 16 17 17 18 19 20 22 The mode is 16

Measures of Central Tendency Draw a grid and fill it in using the information below: Advantages Disadvantages Mean Median Mode Decide which are advantages and disadvantages of each measure of central tendency (see next slide for answers) • • • Very large or very small numbers (anomalies) can distort the answer All the data are used in it’s calculation, making it a powerful measure It must be a number that appears in the data set Is not affected by very large or very small numbers Maybe more than one value, or no value exists. Does not use the actual mathematic data, only the position of the number in the series

Measures of Central Tendency Advantages Disadvantages Mean All the data are used in it’s calculation, making it a powerful measure Very large or very small numbers (anomalies) can distort the answer Median Is not affected by very large or very small number Does not use the actual mathematic data, only the position of the number in the series Mode It must be a number Maybe more than one that appears in the data value, or no value exists. set