These slides are prepared for the students who study statistics .. Under this formula to central tendency is given:

1. MEASURE OF CENTRAL TENDENCY
Mean Median Mode
to

2. One of the most important objectives of a statistical analysis
is to get one single value which represent the entire mass of
data that unique value is called an average value.
The average value lies between the smallest value & the
largest value that central value is also known as measure of
central tendency.
Measure of Central Tendency

3. Types of Measure of Central Tendency
1. Mean (X)
2. Median (Md)
3. Mode (Mo)

4. 1. Arithmetic Mean
The Sum of all observations divided by total number of
observations is called Arithmetic mean.
It is denoted by X & defined as,

5. Individual series
Direct Method Assumed Mean Method
Where, n=total number of observations
X= Variable value
A= Assumed Mean
d= X - A
1. Arithmetic Mean

6. Discrete series
Direct Method Assumed Mean Method
Where, n= 𝛴f
X= Variable value
A= Assumed Mean
d= X - A
1. Arithmetic Mean

7. Continuous series
Direct Method:
Assumed Mean Method:
Step-deviation Method:
Where,
h= class interval
1. Arithmetic Mean

8. 2. Median
If the series is arranging in ascending or descending order of its magnitude then the
value of middle term is called as Median.
It is divided the entire series into equal parts & lies 50% of the distribution so it is
known as positional average.
Median is appropriate to calculate the measure of central tendency or average in
case of open-end class.
And it is also used to test the qualitative data such as intelligence, honesty, beauty
etc.
It is denoted by Md & defined as:

9. Individual series
2. Median
Where,
n= total number of observations for individual series.

10. Discrete series
2. Median
Where,
n= total number of observations for individual series.
n= 𝛴f for discrete series

11. Continuous series
2. Median
If the series to find the median first of all we identify median class by using
formula,
Finally,
Where,
n= 𝛴f
f= frequency
h= height of the class
l= lower limit
c.f.= cumulative frequency

12. 3. Mode
The most repeated value of a group is called mode or the variate value having
the maximum frequency is called mode.
It is used to calculate the most repeated value, most common size, most
common wage etc.
It is unrigidly define average& It is denoted by Mo & defined as:

13. Individual series
3. Mode
If we have unrepeated items in such case to find the mode by using the
following relation:

14. Continuous series
3. Mode
Where,
l = lower limit of the model class
f1 = Frequency of the model class
f0 = Frequency of the pre model class
f2= Frequency of the post model class
h= height of the class

15. 3. Mode
Grouping Method
In abnormal problem to find the mode by using the grouping method.
In grouping method the following steps are used:
Step 1: Prepare the grouping Table.
Step 2: Prepare the analysis table.
Step 3: Use Formula.

16. For Grouping Method
Column I : Frequency itself.
Column II : Sum of two frequencies.
Column III : Leaving first & sum of two frequencies.
Column IV : Sum of three frequencies.
Column V : Leaving first & sum of three frequencies.
Column VI : Leaving first & second & sum of three frequencies.
3. Mode

17. For e.g. Class 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 100-110
f 10 5 15 10 20 22 24 6 2 1
Step 1: Prepare the grouping Table.
Class Col. I (f) Col. II Col. III Col. IV Col. V Col. VI
10-20 10
20-30 6 31
30-40 15 31
40-50 10 45
50-60 20 52
60-70 22 66
70-80 24 52
80-90 6 32
90-100 2 9
100-110 1
16
25
42
30
3
21
30
46
8

18. Step 2: Prepare the analysis table.
Class Col. I Col. II Col. III Col. IV Col. V Col. VI Total
10-20 0
20-30 0
30-40 0
40-50 1
50-60 2
60-70 5
70-80 4
80-90 1
90-100 0
100-110 0
Since , the maximum contribution of the frequency is 5 & which correspond to the model class
60-70. Therefore , M0del Class is (60-70)
3. Mode

19. Step 3: Use Formula
If (f1 < f2) then, we use this formula
Otherwise,
3. Mode

20. Thank You