by the end of this lesson you will be able to explain/calculate the following: 1. mean 2. median 3....

Measures of Central Tendency

By the end of this lesson you will be able to explain/calculate the following:

1. Mean

2. Median

3. Mode

Chance & Data: Statistics

Measures of Central Tendency

Measures of central tendency are summary statistics that measure the middle of the data.

They are defined as:the mean, median and mode.

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 resultMEDIAN: the middle resultMODE: 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

n

xx

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 resultMEDIAN: the middle resultMODE: 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

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 resultMEDIAN: the middle resultMODE: the most frequent result

As this does not give us an exact number we add the 15th and 16th results and divide by 2

Result .

result middle the Find 1st

th

n

5152

1302

1

572

1142

5757

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

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 resultMEDIAN: the middle resultMODE: 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

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 resultMEDIAN: the middle resultMODE: the most frequent result

MEAN: the average result = 55.93MEDIAN: the middle result = 57MODE: 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

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.1. The mean is appropriate when no extreme values or

outliers distort the picture.

2. The median is appropriate when outliers are present.

3. The mode is appropriate when the most common result is significant.