Statistics 2 MEAN MEDIAN MODE
Subject : MATHEMATICS
Class : JSS 1
Term :THIRD TERM
Week : WEEK ELEVEN
Reference Materials
- Scheme of Work
- Online Information
- Textbooks
- Workbooks
- 9 Year Basic Education Curriculum
Previous Knowledge :
The pupils have previous knowledge of
Behavioural Objectives : At the end of the lesson, the pupils should be able to
- say the essence of statistics
- define data
- construct pictogram , bar-chart, pie chart and histogram
WEEK ELEVEN
TOPIC: STATISTICS II
CONTENT: i) The Mean
- ii) The Median
iii) The Mode
INTRODUCTION
Average is the most used word to describe measure of a set of numbers. It is a single value used to represent a set of numbers ( i.e. all values in a set of data).
For example, the average age of students in JSS1 in EDT Schools is 10yrs. This does not mean that every student in JSS1 is 10yrs, but 10 yrs is used to represent the age of all students in JSS1.
The most commonly used statistical averages are arithmetic mean, median and mode.
The Mean
The mean, sometimes called the arithmetic mean, is the most common average. The mean
of a set of numbers or values is found by simply adding all the values together and then divide by the number of the values.
i.e. Mean =sum of values is divided by number of values
Example 1
Find the mean of the following numbers 4, 5, 6, 7, 8.
Solution
Sum of all the numbers = 4 + 5+ 6+ 7+ 8 =30
There are 5 numbers, so divide by 5
Mean = sum of values /number of values=305=6
Example 2
In five tests, a student’s marks were 13, 17, 18, 8 and 10. What is the average mark?
Solution
Average (mean) mark =13+17+18+8+105
= 665 = 13.2
Example 3
A hockey team has played eight games and has a mean score of 3.5 goals per game. How many goals has the team scored?
Solution
Mean score = total number of goals/number of games
- = total number of goals=8
Multiply both sides by 8
Total number of goals = 3.5 x 8
Total number of goals scored = 28
Evaluation
The ages of 10 pupils in a certain class are: 9, 9, 8, 12, 11, 11, 12, 10,9,9
- Calculate the mean age of the pupils.
- How many pupils are less than the mean age?
- How many pupils are above the mean age?
The Median
The median of a set of values or data is the middle value when the data is arranged in order of magnitude or size.
Example 4
Find the median of the following numbers 13, 10, 6, 8, 7, 9, 11
Solution
Arrange the numbers in order of increasing size
6,7,8, 9, 10, 11, 13
The middle value is the fourth number from LHS, i.e. 9 is the median
Note: The result is the same if the numbers are arranged in order of decreasing size
Example 5
Find the median of these numbers: 13, 15, 14, 12, 13, 15, 16, 10, 12, 14
Solution
Arrange the set of numbers in order of increasing size
10, 12, 12, 13, 13, 14, 14, 15, 15, 16
We have even number of values, so there is no middle number. Tp obtain the median, we add the two middle numbers and then divide by 2.
Median = sum of the two middle numbers2
= 13+142 = 1312
Evaluation
A dice was thrown 14 times, and the scores were : 1,6,6,4,3,5,5,2,4,6,3,2,1,4. Find the median score
The Mode
The mode is the value that occurs most frequently in a set of data. A set of data may have more than one mode. When all values occur only once then there is no mode.
Example 6
Find the mode of these numbers 3, 4, 3, 2, 4, 3, 2, 3, 5, 3, 2
Solution
3 occurs 5 times, 4 occurs 2 times, 2 occurs 3 times, 5 occurs 1 time
3 occurs most frequently, so the mode is 3
Note: if there are two modes in a data, the data is said to be bimodal and when there are more than two modes, the data is said to be multimodal.
Presentation
The topic is presented step by step
Step 1:
The class teacher revises the previous topics
Step 2.
He 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
Evaluation
Find the mode of these numbers
- 14, 18, 12, 10, 18, 20,19,14,18,10
- 1,5,6,3,5,7,10,8,4,9
General Evaluation
The table below shows the marks obtained in a Mathematics test by JSS1 students.
| Mark | 5 | 6 | 7 | 8 | 9 | 10 |
| Frequency | 2 | 3 | 5 | 7 | 4 | 2 |
Find the
- Modal mark
- Median mark
- Mean mark of the distribution to 1 d.p
Conclusion :
The class teacher wraps up or conclude the lesson by giving out short note to summarize the topic that he or she has just taught.
The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.
He or she does the necessary corrections when and where the needs arise.
:
Assignment
- A student obtained 50, 80, 60 and 70 marks in 4 different tests in Mathematics. Find the mean score. A. 60 B. 65 C. 70 D. 75
- Find the median of these numbers: 6, 3, 5, 7, 8. A. 3 B. 5 C. 6 D. 5.5
- What is the mode of these numbers: 4,6,8,7,3,1,3,7,1,8,1. A. 7 B. 2 C. 8 D. 1
- The length of 20 metal rods is 1860cm when added together. Find the average length of the rods. A. 91cm B. 90.5 cm C. 93cm D.92cm
- If there are two modes in a data, the data is said to be ……….. A. single modal B. multimodal C. bimodal D. none of the above
Theory
- Zainab did 10 tests in English dictation and her marks were as follows: 70, 50, 60, 75, 30, 65, 60, 40, 78, 80 (a) Find her mean mark (b) Find her median mark (c) Find her modal mark
- Tolu obtained an average of 70 marks in 8 tests. He then scored 65 and 80 marks in another two tests. Find his new average mark
1. The __________ is the sum of all values divided by the total number of values.
(a) Mode
(b) Median
(c) Mean
2. To find the median of a data set, first arrange the data in __________ order.
(a) descending
(b) random
(c) ascending
3. The __________ is the middle value of a data set when arranged in ascending or descending order.
(a) Mean
(b) Mode
(c) Median
4. If there is an odd number of data points, the median is the __________ value.
(a) middle
(b) average
(c) highest
5. If there is an even number of data points, the median is the __________ of the two middle values.
(a) sum
(b) product
(c) average
6. The __________ is the value that appears most frequently in a data set.
(a) Mean
(b) Median
(c) Mode
7. If all the values in a data set are the same, the mode is __________.
(a) unique
(b) zero
(c) not defined
8. The mode can be __________ in a data set if all values occur with the same frequency.
(a) multiple
(b) singular
(c) zero
9. The mean, median, and mode are all measures of __________ tendency.
(a) central
(b) extreme
(c) random
10. To calculate the mean, add up all the values and then divide by the __________.
(a) highest value
(b) total number of values
(c) lowest value
11. The mode is the value with the __________ frequency in a data set.
(a) lowest
(b) highest
(c) middle
12. In an even number of data points, there are __________ middle values for the median.
(a) two
(b) three
(c) none
13. The mean of 10, 15, and 20 is __________.
(a) 10
(b) 15
(c) 20
14. The mode of 5, 8, 8, 10, and 12 is __________.
(a) 5
(b) 8
(c) 10
15. The median of 3, 7, 9, and 15 is __________.
(a) 7
(b) 8
(c) 9