MEASURES OF CENTRAL TENDENCY
These are the values which show the degree to which a given data or any given set of values will converge toward the central point of the data.
Measures of central tendency, also called measures of location, is the statistical information that gives the middle or centre or average of a set of data. Measures of central tendency include arithmetic mean, median and mode.
MEAN: This is the average of variables obtained in a study. It is the most common kind of average. For group data the formula for calculating the mean is ∑fx.
∑f
Where, Ʃ =Summation
F=frequency
X=observation
MEDIAN: It is the middle number in any given distribution. The formula is
Median = L + (N\2Fb)c
f
Where; L = Lower class limit.
N = Summation 0f the frequency.
Fb = Cumulative frequency before the median class.
f = frequency of the median class.
c= Class size.
MODE: It is the number that appears most in any given distribution, i.e the number with the greatest frequency. When a series has more than one mode,say two,it is said to be bimodal or trimodal for three.
Mode= L + D1
D1+D2
Where, M=mode
L=the lower class boundary of the modal class.
D1=the frequency of the modal class minus the frequency of the class before the modal class.
D2=the frequency of the modal class minus the frequency of the class after it.
C=the width of the modal class.
Example: The table below shows the marks of students of JSS 3 mathematics.
Marks 
15  610  1115  1620  2125  2630 
Frequency  2  3  4  5  6  7 
Use the information above to calculate the following:
 the mean
 the median
 the mode
Solution
mark frequency midpoint fx
15  2  3  6 
610  3  8  24 
1115  4  13  52 
1620  5  18  90 
2125  6  23  138 
2630

7  28  196 
27 506
 A. Mean= ∑fx = 506\27
Ʃf =18.7
 B. median
Mark  F  Cf 
15  2  2 
610  3  5 
1115  4  9 
1620  5  14 
2125  6  20 
2630  7  27 
L1= 15.5
N\2 =27\2=13.5
Fb =9
F =5
C= 5
M=15.5+ (13.59)5
5
M=20
 C. mode= L+ D1
D1+D2
L1=20.5
D1=76=1
D2=70=7
C=5
M=25.5+ (1\1+7)5
M=26.125.
EVALUATION
The table below shows the weekly profit in naira from a minimarket.
You are required to calculate:
 The mean.
 The median.
 The mode.
Weekly profit(#)  110  1120  2130  3140  4150  5160 
Frequency  6  6  12  11  10  5 
READING ASSIGNMENT
 Amplified and Simplified Economics for SSS by Femi Alonge page 2930.
 Further Mathematics Scholastics Series page 265265.
GENERAL EVALUATION QUESTIONS
 Outline the merits of a Joint Stock Company.
 Describe the problems facing Agriculture in Nigeria.
 Outline the main features of Malthusian theory of Population.
 What is money?
 List five characteristics of money.
WEEKEND ASSIGNMENT
 Which of the following is not a set of measure of central tendency? (a) mode and mean (b) mean and median (c) mean and percentile (d) mode and median
 The most frequently occurring value in a give data is (a) mean ( b ) mode (c ) range (d) median.
 The formula (n+1)th is for calculating (a ) median (b ) mode (c ) mean (d) range.
2
 The L1 in the formula for the calculation of measures of location represents……… (a) lower class boundary of the median class (b) actual frequency of the modal class (c) upper class boundary of the median class (d) frequency of the class just after the median class
 The formation of cumulative frequency is necessary for the calculation of………… (a) mean (b) range (c) median (d) mode
SECTION B
The following table shows the distribution of marks scored by a class of students in a promotion examination.
Marks  Number of students 
1029  6 
3039  5 
4049  7 
5059  10 
6069  5 
7079  4 
8089  3 
 Calculate the mean mark.
 Find the mode.
See also