Basic Tools Of Economic Analysis II SS1 Economics Lesson Note

MEASURES OF CENTRAL TENDENCY

1. Mean
2. Median 
3. Mode

 Measures of central tendency means are 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. It is also called a measure of location and is the statistical information that gives the middle centre or average of a set of data. It includes mean, median and mode. 

THE MEAN

The mean or arithmetic mean is defined as the sum of a series of figures divided by the number of observations. It is the most common and the most widely used among the other types of averages or measures of central tendency.

TYPES OF MEAN

1. The Arithmetic Mean
2. The Geometric Mean
3. The Quadratic Mean

Example

Calculate the arithmetic mean of the following scores of eight students in an economics test. The scores are 14, 18, 24, 16, 30, 12, 20, and 10.

Solution

Step 1: Add up the scores

14+18+24+16+30+12+20+10 = 144

Step 2: Number of observations (students) = 8

Arithmetic Mean =Sum of observations divided by Number of observations

                           =   144      = 18

                                   8

ADVANTAGES OF THE MEAN

1. It is easy to derive or calculate.
2. It is easy to interpret.
3. It is the best-known average. 
4. It has a determinate exact value.
5. It provides a good measure of comparison.

DISADVANTAGES OF THE MEAN

1. It is difficult to determine without calculation.
2. Some facts may be concealed.
3. It cannot be obtained graphically.
4. If one or more values are incorrect or missing, the calculation becomes difficult.
5. It may lead to distorted results.

THE MEDIAN

The median is an average which is the middle value when figures are arranged in their order of magnitude either in ascending or descending order, especially from ungrouped data.

Example 1:

Calculate the median of the following scores: 12, 8 15, 9, 3, 7, and 1

Solution

Step 1:   First, arrange in order

                           1, 3, 7, 8, 9, 12 and 15

Step 2:                Total frequency is 7, thus the middle number in the set is in the 4th position

Step 3:                Median = 4th Position = 8

Example 2:

Find the median of this set of numbers; 36, 42, 10, 15, 9, 32 16 and 12.

Solution 

Step 1:       9, 10, 12, 15, 16, 32 36 and 42

Step 2:      Total Frequency = 8

Step 3:   Median = 4th and 5th Position 

= 4th + 5th =  15 + 16

                    2

=  31 = 15.5

                2

ADVANTAGES OF THE MEDIAN

1. It is easy to determine with little or no calculations
2. It is easy to understand and compute 
3. It does not use all values in the distribution 
4. It gives a clear idea of the distribution 

DISADVANTAGES OF THE MEDIAN

1. It is not useful in further statistical calculation
2. It ignores very large or small values
3. It does not represent a true average of the set of data.

THE MODE

This is the most frequently recurring number in a set of numbers or data, that is to say, it is the number or value with the highest frequency. It tells us the most popular observation. The best and easiest way of calculating the mode of any distribution is to form a frequency table for it.

Example

Using the frequency distribution of example 3 above, the mode is 3 because it has the highest frequency of six (6)

MERITS

1. It can be easily understood.
2. It is not affected by extreme values. 
3. Easy to calculate from the graph.
4. It is easy to determine.

DEMERIT

1. It can be a poor average. 
2. It can be difficult to compute if more than one mode exists.
3. It is not useful in further statistical calculations.
4. All the values used in the distribution are not considered.

ASSIGNMENT 

1. Find the mean of the following set of numbers 14,11,12,13,11,14,12,20,24,21,22,23,20,11,13,23.
2. Define the median.  
3. b) State four advantages of median.
4. Calculate the mean 18,14,14,15,13,18,19,19,19,21.
5. b) What are the disadvantages of the mean?
6. Define the mode.
7. b) List three advantages of the mode