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\2-Fb)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 bi-modal or tri-modal 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 |
1-5 | 6-10 | 11-15 | 16-20 | 21-25 | 26-30 |
| Frequency | 2 | 3 | 4 | 5 | 6 | 7 |
Use the information above to calculate the following:
- the mean
- the median
- the mode
Solution
mark frequency mid-point fx
| 1-5 | 2 | 3 | 6 |
| 6-10 | 3 | 8 | 24 |
| 11-15 | 4 | 13 | 52 |
| 16-20 | 5 | 18 | 90 |
| 21-25 | 6 | 23 | 138 |
| 26-30
|
7 | 28 | 196 |
27 506
- A. Mean= ∑fx = 506\27
Ʃf =18.7
- B. median
| Mark | F | Cf |
| 1-5 | 2 | 2 |
| 6-10 | 3 | 5 |
| 11-15 | 4 | 9 |
| 16-20 | 5 | 14 |
| 21-25 | 6 | 20 |
| 26-30 | 7 | 27 |
L1= 15.5
N\2 =27\2=13.5
Fb =9
F =5
C= 5
M=15.5+ (13.5-9)5
5
M=20
- C. mode= L+ D1
D1+D2
L1=20.5
D1=7-6=1
D2=7-0=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 mini-market.
You are required to calculate:
- The mean.
- The median.
- The mode.
| Weekly profit(#) | 1-10 | 11-20 | 21-30 | 31-40 | 41-50 | 51-60 |
| Frequency | 6 | 6 | 12 | 11 | 10 | 5 |
READING ASSIGNMENT
- Amplified and Simplified Economics for SSS by Femi Alonge page 29-30.
- Further Mathematics Scholastics Series page 265-265.
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 |
| 10-29 | 6 |
| 30-39 | 5 |
| 40-49 | 7 |
| 50-59 | 10 |
| 60-69 | 5 |
| 70-79 | 4 |
| 80-89 | 3 |
- Calculate the mean mark.
- Find the mode.
See also