# Measures of central tendencies

Subject:

### MATHEMATICS

Term:

First Term

Week:

Week 9

Class:

JSS 3 / BASIC 9

Previous lesson: Pupils have previous knowledge of

### Data presentation (Revision) Range of a set of values

that was taught in their previous lesson

Topic:Measures of central tendencies

Behavioural Objectives:

At the end of the lesson, learners will be able to

• Explain mean
• Explain media
• Solve simple mathematics questions mean, median and mode

Instructional Materials:

• Wall charts
• Pictures
• Related Online Video
• Flash Cards

Methods of Teaching:

• Class Discussion
• Group Discussion
• Explanation
• Role Modelling
• Role Delegation

Reference Materials:

• Scheme of Work
• Online Information
• Textbooks
• Workbooks
• 9 Year Basic Education Curriculum
• Workbooks

CONTENT:

WEEK 9

TOPIC: Measures of central tendencies

CONTENT:

• Mean
• Median
• Mode

Mean: The average score of a given data.

Median: The score at the middle after rearranging either ascending or

descending order.

Mode: The score with the highest frequency.

Examples:

1. Find the measures of central tendency of the data below.

8, 10, 13, 11, 7, 8, 2, 8, 6

Solution:

Mean:

To find the mean of the data above, you may not need to rearrange. Just add up the data and divide by the total number they are.

Mean

Median:

First rearrange the data either in ascending or descending order.

Ascending order: 2, 6, 7, 8, 8, 8, 10, 11, 13

Descending order: 13, 11, 10, 8, 8, 8, 7, 6, 2

Using median position:( )th

Where is the number of data.

Median position th 5th  (Meaning that, the median is at the 5th position). Count 5 from any of the ends.

Hence, the median = 8

Mode:

Mode is the number or score that appears most, i.e, number or score with the highest frequency.

Since ‘8’ appears most, hence, the mode is 8.

1. The below table shows the age of under 18 youths caught taking Indian hemp by the police at a T-junction near Olobeja with the following frequency of wrapped Indian hemp found in their possession.
 Age(yrs) 13 14 15 16 17 Frequency of wrapped Indian hemp 1 2 5 7 15

Find the: (i) Mean (ii) Median (iii) Mode of the frequency of the wrapped Indian hemp.

Solution:

Since the data are many, adding up the numbers and then divide by the total number would take a lot of time. So, we need a frequency table.

 Age Frequency Cumulative  frequency 13 1 1 13 14 2 3 28 15 5 8 75 16 7 15 112 17 15 30 255 TOTALS Ʃ Ʃ 483

The total sum of frequency must be the same with the last number in the cumulative frequency column, that is, 30.

Mean

Mean

Median

First and foremost, let’s find the position of the median.

Position )th th

We count ‘15.5th’ position along the frequency column from any of the ends.

It lies in the age ‘16’. Hence, the median is 16yrs.

Mode

Check for the highest frequency along the frequency column.

It is ‘15’. Right?

What age has 15?

Hence, the mode is 17yrs

1. The marks of 20 students in a mathematics test score out of 10 are as follows:

5, 8, 6, 7, 4, 9, 5, 7, 7, 0, 2, 1, 3, 9, 8, 4, 6, 7, 8, 1

Prepare a frequency table for the distribution and find the measure of central tendency.

Solution:

 Score Frequency Tally 0 1 / 1 0 1 2 // 3 2 2 1 / 4 2 3 1 / 5 3 4 2 // 7 8 5 2 // 9 10 6 2 // 11 12 7 4 //// 15 28 8 3 /// 18 24 9 2 // 20 18 Ʃ 20 Ʃ 107

Mean

Median

position )th   10.5th position.

By counting 10.5th from any of the ends,

The median = 6.

Mode

The mode = 7.

Class Activity

1. The following figures represent the number of voters that voted from 2003 to 2008.
 YEAR NO. OF VOTERS 2003 89,000 2004 101,000 2005 115,000 2006 131,000 2007 151,000 2008 96,000

a). What is the total number of voters?

b). Find the mean of the voters.

c). In what year did the people vote most?

d). In what year did the people vote least?

e). How many people voted in years 2003 and 2004?

1. The total votes cast at different centers are as follows:

5000, 7000, 9000, 10000, 12000, 17000, 18000, 15000, 9000, 18000.

Find:

1. The mean of the votes cast.
2. The median of the votes cast.
3. The mode of the votes cast.

ASSIGNMENT

Use the knowledge of measures of central tendency to analyze the information on drug abuse.

1. The following data represent the frequencies at which some senior secondary students abuse drugs.

a). 33, 5, 8, 8, 10, 10, 10, 13, 15.

b). 4, 8, 9, 10, 13, 13, 15, 16, 16.

Find the mode for the drug abuse. What is its significant?

1. The table below shows the rate at which some teenagers abuse drugs:
 Name Ade Uche Adamu Bako Binta Frequency 12 13 15 13 12

Find the mode for the drug abuse.

1. The following data shows the ages of some youths that take drugs:

23yrs,  19yrs,   18yrs,  30yrs

15yrs,  21yrs,    19yrs,  24yrs

25yrs,  31yrs,    17yrs,   20yrs

1. Find the median ages of the youths that take drugs.
2. Find the mean age of the youth.

PRESENTATION:

Step 1:

The subject teacher revises the previous topic

Step 2:

He or she introduces the new topic

Step 3:

The class teacher allows the pupils to give their own examples and he corrects them when the needs arise

CONCLUSION:

The subject goes round to mark the pupil’s notes. He does the necessary corrections

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