MEASURES OF STATISTICAL AVERAGE | MEASURES OF CENTRAL TENDENCY

Measures of central tendency or statistical average are considered as the typical value for the entire data. It is the single value that describes the characteristics of the entire group.

MEAN

Mean is the most common measure of statistical average. It is also known as arithmetic average.

We can define the mean as ‘the value which is obtained by dividing the total values of all the items in a series by the total number of items’.

 

Mean x = Sum x / n

Where,

Sum x = total value of the items

n = total number of items

Sometimes instead of calculating the simple mean, the researcher has to assess the weighted mean or the frequency means for a statistical average.

 

EXAMPLES

Find the arithmetic mean of the following:

7, 9, 12, 14, 17, 20

Solution:

X = 7 + 9 + 12 +14 + 17 + 20

                         6

X = 79

       6

X = 13.17

 

Calculate the arithmetic average / mean from the following

Family	A	B	C	D	E	F	G	H	I
Daily Income	500	750	250	300	1000	800	100	600	80

 

Individual = n	Income = x
A B C D E F G H I	500 750 250 300 1000 800 100 600 80
Total = 9	Sum X = 4380

 

X = sum X / n

   = 4380 / 9

   = 486.67

 

Calculate the arithmetic mean from the following:

Daily Wages	No. of Workers
50.5-55.5	12
55.5-60.5	8
60.5-65.5	14
65.5-70.5	20
70.5-75.5	25
75.5-80.5	6
80.5-85.5	10

 

 Solution: 

Daily Wages	Mid value (x)	No. of Workers (f)	F x
50.5-55.5	53	12	636
55.5-60.5	58	8	464
60.5-65.5	63	14	882
65.5-70.5	68	20	1360
70.5-75.5	73	25	1825
75.5-80.5	78	6	468
80.5-85.5	83	10	830

 

N = 95

Sum fx = 6465

X = sum fx / n

   = 6465/95

   = 68.05

 

 

 

MEDIAN

Median can be defined as the value of the item which divides the series into two equal parts.

Median is the value of the middle item of series when it is arranged in ascending or descending order.

 Median = sum of N+1th item  

                                2

Example:

Determine the median of the following items

50, 74, 80, 85, 95,100, 106

Solution:

Median = sum of N+1th item  

                                2

M = 7 + 1

           2

= 8 / 2

= 4

85 is the median

 

MODE

Mode is the value which occurs more frequently in a distribution.

Example

5, 8, 3, 9, 13, 9, 20, 15, 9, 18, 25

Mode = 9 

Comparison of Mean, Median, and Mode

Mean	Median	Mode
Defined as the arithmetic average of all observations in the data set.	Defined as the middle value in the data set arranged in ascending or descending order.	Defined as the most frequently occurring value in the distribution; it has the largest frequency.
Requires measurement on all observations.	It does not require measurement on all observations.	It does not require measurement on all observations.
Uniquely and comprehensively defined.	Cannot be determined under all conditions.	Not uniquely defined for multi-modal situations.
Affected by extreme values.	Not affected by extreme values.	Not affected by extreme values.
Can be treated algebraically. In other words, Means of several groups can be combined.	Cannot be treated algebraically, meaning, Medians of several groups cannot be combined.	Cannot be treated algebraically, since Modes of several groups cannot be combined.