This document provides information about measures of central tendency including the mode, mean, and median. The mode is the data value that occurs most frequently in a data set. The mean is the average of the values, found by summing all values and dividing by the total number of data points. The median is the middle value when data points are arranged in order. Examples are given of calculating the mode, mean, and median from data sets presented in tables.

1. Mode
The value (data point) that occurs the most in a set of
values (data) or is the data point with the largest
frequency

2. MEAN
𝒙 𝑥1 𝑥2 𝑥3 𝑥4
𝑓(𝑥) 𝑓1 𝑓2 𝑓3 𝑓4
The mean of a set of numbers is the average of the numbers.
𝑥1, 𝑥2, 𝑥3, … , 𝑥 𝑛
𝑋 =
𝑥
𝑛
If data set is given in a frequency table,
Then, 𝑋 =
𝑓𝑥
𝑓

3. MEAN
𝒙 𝑥1 𝑥2 𝑥3 𝑥4
𝑓(𝑥) 𝑓1 𝑓2 𝑓3 𝑓4
Then, 𝑋 = 𝐴 +
𝑓𝑑
𝑓
If a guess is made at the mean, say 𝐴 and the difference
between A and 𝑥𝑖 is 𝑑𝑖.

4. The mean of 2 − 𝑡, 4 + 𝑡, 3 − 2𝑡, 2 + 𝑡 and 𝑡 −
1 is.
JAMB 2018
SOLUTION
Mean, 𝑋 =
𝑥
𝑛
=
2 − 𝑡 + 4 + 𝑡 + 3 − 2𝑡 + 2 + 𝑡 + (𝑡 − 1)
5
2 + 4 + 3 + 2 − 1 − 𝑡 + 𝑡 − 2𝑡 + 𝑡 + 𝑡
5
10 + 0
5
10
2
= 2

5. The distribution of scores in a class test are as follows: 2,8,6,5,8,6,6,5,6 and 5. Find
the product of the modal and the median score
JAMB 2018
SOLUTION
6 occurs most
Modal mark= 6
For median mark, we arrange the numbers in order:
2,5,5,5,6,6,6,6,8,8
Median mark =
6+_6
2
12
2
= 6
Their product = 6 × 6 = 36

6. Four pupils have an average age of 12years and two other pupils of average age of 10.5years are added. What is
the average age of the six pupils?
A. 10.5yrs.
B. 11yrs.
C. 11.5 yrs.
D. 12yrs.
E. 12.5yrs.
NECO 2014
SOLUTION
𝑇ℎ𝑒 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑎𝑔𝑒 =
12 × 4 + 2 × 10.5
4 + 2
= 11.5𝑦𝑟𝑠

7. If the mean of the following set of data, 2, 3,3,3, 2,4 ,4 and 3 is divided by its mode, the result is:
A. 1
B. 2
C. 3
D. 5
E. 8
NECO 2014
SOLUTION
𝑇ℎ𝑒 𝑚𝑒𝑎𝑛 =
2 + 3 + 3 + 3 + 4 + 4 + 3
8
= 3
The mode = 3
𝑚𝑒𝑎𝑛
𝑚𝑜𝑑𝑒
=
3
3
= 1

8. 1. In a mid-term test conducted for a certain class, the total score out of 10 was 60, if
the mean score was 4, Find the number of student in the class.
A. 12
B. 15
C. 18
D. 20
E. 6
The correct answer is 15

9. 2. If
𝑥
𝑛
= 6, and
𝑥+3
𝑛+1
= 5. Find the value of 𝑛.
A. 0
B. 1
C. 2
D. 3
E. 5
The correct answer is 2

10. 3. The table below is a distribution of marks scored by 20 students out 10.
What is the Median score?
A. 4
B. 5
C. 6
D. 7
E. 8
The correct answer is 6
𝑴𝒂𝒓𝒌𝒔 (𝒙) 𝟒 𝟓 𝟔 𝟕 𝟖
𝑁𝑜. 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 6 3 4 3 4

11. 4. The table below is a distribution of marks scored by 20 students out 10.
What is the average score?
A. 4.8
B. 5.8
C. 6.8
D. 7.8
E. 8.8
The correct answer is 5.8
𝑴𝒂𝒓𝒌𝒔 (𝒙) 𝟒 𝟓 𝟔 𝟕 𝟖
𝑁𝑜. 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 6 3 4 3 4

12. 5. The table below is a distribution of marks scored by 20 students out 10.
What is the modal mark?
A. 4
B. 5
C. 6
D. 7
E. 8
The correct answer is 4
𝑴𝒂𝒓𝒌𝒔 (𝒙) 𝟒 𝟓 𝟔 𝟕 𝟖
𝑁𝑜. 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 6 3 4 3 4

13. 6. If 𝑥 + 𝑦 + 𝑧 = 30, Find the mean of 𝑥 + 4, 𝑦 + 5,and 𝑧 + 5.
A. 8
B. 7
C. 6
D. 5
E. 4
The correct answer is 4

14. 7. If the mean of 𝑥 𝑎𝑛𝑑 𝑦 𝑖𝑠 30, and y is 2 times 𝑥, Find the value of 𝑥.
A. 10
B. 20
C. 30
D. 40
E. 50
The correct answer is 20

15. 8. The table below is a distribution of marks scored by students in a test.
What is the value of 𝑦 if the average score was 2
2
3
?
A. 4
B. 5
C. 6
D. 7
E. 8
The correct answer is 7
𝑴𝒂𝒓𝒌𝒔 (𝒙) 𝟏 𝟐 𝟑 𝟒 𝟓
𝑁𝑜. 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 6 𝑦 1 2 5

16. 9. Which data set has a mode of 4, mean of 3
2
3
and median of 3.5?
A. 4,4,3,3,2,6,4
B. 4,5,4,7,8,1
C. 6,4,4,2,3,4
D. 8,4,3,4,2,1
E. 8,4,3,4,2,1,0
The correct answer is 8,4,3,4,2,1

17. 10. The table below is a distribution of marks scored by 20 students.
Calculate the value of 𝑥.
A. 2
B. 3
C. 4
D. 5
E. 1
The correct answer is 2
𝑴𝒂𝒓𝒌𝒔 (𝒙) 𝟏 𝟐 𝟑 𝟒 𝟓
𝑁𝑜. 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 4 3 4 7 𝑥

18. SUMMARY
The median is a measure of central tendency.
To find the median, we arrange the data in ascending or
descending order.
If there is an odd number of data, the median is the middle
value. • If there is an even number of data, the median is the
average of the two middle data points.

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