# Measures of Central Tendency

## Definition of Measures of Central Tendency

A measure of central tendency is a measure that tells us where the middle of a bunch of data lies.

The three most common measures of central tendency are the mean, the median, and the mode.

### More About Measures of Central Tendency

Mean: Mean is the most common measure of central tendency. It is simply the sum of the numbers divided by the number of numbers in a set of data. This is also known as average.

Median: Median is the number present in the middle when the numbers in a set of data are arranged in ascending or descending order. If the number of numbers in a data set is even, then the median is the mean of the two middle numbers.

Mode: Mode is the value that occurs most frequently in a set of data.

### Examples of Measures of Central Tendency

For the data 1, 2, 3, 4, 5, 5, 6, 7, 8 the measures of central tendency are

Mean =

Median = 5

Mode = 5

### Video Examples: Measures of Central Tendency

### Solved Example on Measures of Central Tendency

**Ques: **Find the measures of central tendency for the data set 3, 7, 9, 4, 5, 4, 6, 7, and 9.

##### Choices:

- A. Mean = 6, median = 6 and modes are 4, 7 and 9
- B. Mean = 6, median = 6 and mode is 4
- C. Mean = 6, median = 6 and modes are 4 and 9
- D. Mean = 6, median = 9 and modes are 4, 7 and 9

Correct Answer: A

### Solution:

- Step 1: Mean, median and mode of a data set are the measures of central tendency.
- Step 2: Mean of the data set = [Formula.]
- Step 3: [Substitute the values.]
- Step 4: [Add the data values in the numerator and divide.]
- Step 5: The data set in the ascending order is 3, 4, 4, 5, 6, 7, 7, 9, and 9. So, Median of the set is 6. [Median is the middle data value of the ordered set.]
- Step 6: Mode is/are the data value(s) that appear most often in the data set. So, the modes of the data set are 4, 7 and 9.
- Step 7: So, the measures of central tendency of the given set of data are mean = 6, median = 6 and modes are 4, 7, and 9.