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
- Asking Questions
- 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:
- 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} 5^{th} (Meaning that, the median is at the 5^{th} 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.
- 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 ‘15.5^{th}’ 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
- 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} 10.5^{th} position.
By counting 10.5^{th} from any of the ends,
The median = 6.
Mode
The mode = 7.
Class Activity
- 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?
- The total votes cast at different centers are as follows:
5000, 7000, 9000, 10000, 12000, 17000, 18000, 15000, 9000, 18000.
Find:
- The mean of the votes cast.
- The median of the votes cast.
- The mode of the votes cast.
ASSIGNMENT
Use the knowledge of measures of central tendency to analyze the information on drug abuse.
- 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?
- 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.
- The following data shows the ages of some youths that take drugs:
23yrs, 19yrs, 18yrs, 30yrs
15yrs, 21yrs, 19yrs, 24yrs
25yrs, 31yrs, 17yrs, 20yrs
- Find the median ages of the youths that take drugs.
- 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