# Lesson Notes By Weeks and Term - Junior Secondary School 1

STATISTICS II

SUBJECT: MATHEMATICS

CLASS:  JSS 1

DATE:

TERM: 3rd TERM

REFERENCE TEXTBOOKS

• New General Mathematics, Junior Secondary School Book 1
• Essential Mathematics for Junior Secondary School Book 1

WEEK ELEVEN

TOPIC: STATISTICS II

CONTENT:    i) The Mean

1. 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 Good Shepherd 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 valuesnumber 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 valuesnumber 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 goalsnumber of games

1. = total number of goals8

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

1. Calculate the mean age of the pupils.
2. How many pupils are less than the mean age?
3. 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.

Evaluation

Find the mode of these numbers

1. 14, 18, 12, 10, 18, 20,19,14,18,10
2. 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

1. Modal mark
2. Median mark
3. Mean mark of the distribution to 1 d.p

1. Essential Mathematics for JSS1 by A.J.S Oluwasanmipg 270-275
2. NGM for JSS1 by MF Macrae, et. al pg179-184

Weekend Assignment

1. 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
2. Find the median of these numbers: 6, 3, 5, 7, 8.  A. 3  B. 5   C. 6  D. 5.5
3. 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
4. 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
5. 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

1. 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
2. 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.