CLASS: JSS 1
TERM: 3rd TERM
TOPIC: STATISTICS II
CONTENT: i) The Mean
iii) The Mode
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, 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
Find the mean of the following numbers 4, 5, 6, 7, 8.
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
In five tests, a student’s marks were 13, 17, 18, 8 and 10. What is the average mark?
Average (mean) mark =13+17+18+8+105
= 665 = 13.2
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?
Mean score = total number of goalsnumber of games
Multiply both sides by 8
Total number of goals = 3.5 x 8
Total number of goals scored = 28
The ages of 10 pupils in a certain class are: 9, 9, 8, 12, 11, 11, 12, 10,9,9
The median of a set of values or data is the middle value when the data is arranged in order of magnitude or size.
Find the median of the following numbers 13, 10, 6, 8, 7, 9, 11
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
Find the median of these numbers: 13, 15, 14, 12, 13, 15, 16, 10, 12, 14
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
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 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.
Find the mode of these numbers 3, 4, 3, 2, 4, 3, 2, 3, 5, 3, 2
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.
Find the mode of these numbers
The table below shows the marks obtained in a Mathematics test by JSS1 students.
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