1. By the end of this lesson you will be able to explain/calculate the following: 1. Mean 2. Median 3. Mode

2. Measures of Central Tendency Measures of central tendency summary statisticsmiddle Measures of central tendency are summary statistics that measure the middle of the data. They are defined as: the mean, median and mode.

3. The following set of data shows the number of lollies in each of thirty 500 g bags. Find the mean, median, and mode. 59, 62, 51, 55, 46, 60, 58, 49, 64, 57, 53, 50, 56, 61, 54, 53, 58, 58, 61, 58, 54, 52, 57, 58, 59, 51, 48, 60, 60, 56 Measures of central tendency help us to find the most common result. The three measures of central tendency are: MEAN: the average result MEDIAN: the middle result MODE: the most frequent result First order the numbers from smallest to biggest: 46, 48, 49, 50, 51, 51, 52, 53, 53, 54, 54, 55, 56, 56, 57, 57, 58, 58, 58, 58, 58, 59, 59, 60, 60, 60, 61, 61, 62, 64, Worked Example

4. The following set of data shows the number of lollies in each of thirty 500 g bags. Find the mean, median, and mode. Measures of central tendency help us to find the most common result. The three measures of central tendency are: MEAN: the average result MEDIAN: the middle result MODE: the most frequent result Add all results up = 1678 Then divide by how many results there are, = 1678/30 = 55.93 Worked Example 46, 48, 49, 50, 51, 51, 52, 53, 53, 54, 54, 55, 56, 56, 57, 57, 58, 58, 58, 58, 58, 59, 59, 60, 60, 60, 61, 61, 62, 64

5. The following set of data shows the number of lollies in each of thirty 500 g bags. Find the mean, median, and mode. Measures of central tendency help us to find the most common result. The three measures of central tendency are: MEAN: the average result MEDIAN: the middle result MODE: the most frequent result As this does not give us an exact number we add the 15 th and 16 th results and divide by 2 46, 48, 49, 50, 51, 51, 52, 53, 53, 54, 54, 55, 56, 56, 57, 57, 58, 58, 58, 58, 58, 59, 59, 60, 60, 60, 61, 61, 62, 64 Worked Example

6. The following set of data shows the number of lollies in each of thirty 500 g bags. Find the mean, median, and mode. Measures of central tendency help us to find the most common result. The three measures of central tendency are: MEAN: the average result MEDIAN: the middle result MODE: the most frequent result Worked Example 46, 48, 49, 50, 51, 51, 52, 53, 53, 54, 54, 55, 56, 56, 57, 57, 58, 58, 58, 58, 58, 59, 59, 60, 60, 60, 61, 61, 62, 64

7. The following set of data shows the number of lollies in each of thirty 500 g bags. Find the mean, median, and mode. Measures of central tendency help us to find the most common result. The three measures of central tendency are: MEAN: the average result MEDIAN: the middle result MODE: the most frequent result MEAN: the average result = 55.93 MEDIAN: the middle result = 57 MODE: the most frequent result = 58 Worked Example 46, 48, 49, 50, 51, 51, 52, 53, 53, 54, 54, 55, 56, 56, 57, 57, 58, 58, 58, 58, 58, 59, 59, 60, 60, 60, 61, 61, 62, 64

8. Which to use? Now that we have discussed the three measures of central tendency, it is important to know which measure will be most useful in a given situation. mean 1. The mean is appropriate when no extreme values or outliers distort the picture. median 2. The median is appropriate when outliers are present. mode 3. The mode is appropriate when the most common result is significant.