Basic Tools For Economic Analysis SS2 Economics Lesson Note

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, are the statistical information that gives the middle centre or average of a set of data. Measures of central tendency include arithmetic mean, median and mode.

1. 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

2. 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.

3. 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

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.

Use the information above to calculate the following:                 

1. the mean
2. the median
3. the mode

Solution:

Total:  F= 27                           fx=  506

1. Mean= ∑fx = 506 ÷ 27 

                   Ʃf =18.7

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

1. 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.