# Measures of Central Tendency

**MATHEMATICS **

**EVERYDAY STATISTICS **

**TOPIC:** Measures of Central Tendency

**PERFORMANCE OBJECTIVES**

By the end of the lesson, the pupils should have attained the following objectives (cognitive, affective and psychomotor):

- find the mode and median of data;
- calculate the mean of given data.

**ENTRY BEHAVIOR**

The pupils are required to already learned population.

**INSTRUCTIONAL MATERIALS**

The teacher will teach the aid of data chat set of data.

**METHOD OF TEACHING **

**MAIN REFERENCE MATERIALS**

- Prime Mathematics book 6, page
- New Method Mathematics book 6, page

**CONTENT OF THE LESSON**

**LESSON **

**PERIOD: **

**DATE: **

**TIME:**

**INTRODUCTION** **(MEANING) **

**MEASURES OF CENTRAL OF TENDENCY **

A measure of central tendency (also referred to as measures of centre or central location) is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or centre of its distribution.

There are three main measures of central tendency:

- mode
- median
- mean

Each of these measures describes a different indication of the typical or central value in the distribution.

**MODE**

The mode is the most commonly occurring value in a distribution.

Consider this dataset showing the retirement age of 11 people, in whole years:

54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60

This table shows a simple frequency distribution of the retirement age data.

The most commonly occurring value is 54, therefore the mode of this distribution is 54 years.

**LESSON **

**PERIOD: **

**DATE: **

**TIME:**

**MEDIAN**

The median is the middle value in distribution when the values are arranged in ascending or descending order.

The median divides the distribution in half (there are 50% of observations on either side of the median value). In a distribution with an odd number of observations, the median value is the middle value.

Looking at the retirement age distribution (which has 11 observations), the median is the middle value, which is 57 years:

54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60

When the distribution has an even number of observations, the median value is the mean of the two middle values. In the following distribution, the two middle values are 56 and 57, therefore the median equals 56.5 years:

52, 54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60

**LESSON **

**PERIOD: **

**DATE: **

**TIME:**

**MEAN**

The mean is the sum of the value of each observation in a dataset divided by the number of observations. This is also known as the arithmetic average.

Looking at the retirement age distribution again:

54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60

The mean is calculated by adding together all the values (54+54+54+55+56+57+57+58+58+60+60 = 623) and dividing by the number of observations (11) which equals 56.6 years.

**LESSON **

**PERIOD: **

**DATE: **

**TIME:**

**LESSON EVALUATION**

Given the scores of first year students in a Statistics test – 10, 5, 9, 8, 6, 5, 9, 8, 7, 6 and 5. Organize data and find the:

- mode
- median
- mean

Revision and summary of the lesson.

**PRESENTATION**

To deliver the lesson, the teacher adopts the following steps:

- To introduce the lesson, the teacher revises the previous lesson. Based on this, he/she asks the pupils some questions;
- Guides the pupils to collect and summarize data and indicate the mode and find the median;
- Pupil’s Activities – organize a given data and indicate the mode and find the median.
- Guides pupils to organize a given data and calculate the mean.
- Pupil’s Activities – organize a given data and calculate the mean.

**CONCLUSION**

To conclude the lesson for the week, the teacher revises the entire lesson and links it to the following week’s lesson.

**LESSON EVALUATION**

**Pupils to **

- Organize a given data and find the mode and median;
- Organize a given data and calculate the mean.