statistical methods of decision making

1. Topic:- Measures of Central Tendency
Submitted To-
• Dr. Ashish Singh
(Professor)
Institute of Management Studies,
(Faculty of Management Studies)
BHU, Varanasi.
Submitted By
• Ananya Das
• Anish Chandan
• Simu Singh
Semester- 1st semester
Course- MBA (Agribusiness)
Batch- 2021-23
Subject- Statistical Method for Decision Making
Statistical Method for Decision Making

2. Content
• Measures Of Central Tendency
• Types Of Central Tendency
• Mean
• Median
• Mode

3. Measures of Central Tendency
• Measures of Central Tendency are numerical
descriptive measures which indicate or locate the
Centre of a distribution.
• It is usually called as the averages.
• Importance:-
1) To find representative value.
2) To make the data more concise.
3) To make comparisons.

4. Types of Central Tendency:-
1)Mean
2)Median
3)Mode

5. Mean
•The most commonly used measure of central tendency is
called the mean (denoted by for a sample, and µ for a
population).
•The mean is the same of what many of us call the
‘average’, and it is calculated in the following manner:-
X
X
X
N


X

6. • Some measures of mean used to find the central tendency are as follows:-
Geometric Mean
Geometric Mean = 𝑋1·𝑋2· … ·𝑋𝑛 or Geometric Mean = (x₁ · x₂ · ... · xₙ)1/n
Harmonic Mean

7. Assumed Mean Method
• Assumed mean is calculated by:-
Were:
• a = assumed mean
• fi = frequency of ith class
• di = xi – a = deviation of ith class
• Σfi = n = Total number of observations
• xi = class mark = (upper class limit + lower class limit)/2

8. Example:
The following table gives information about the marks obtained by 110 students in an
examination. Find the mean marks of the students using the assumed mean method
Class 0-10 10-20 20-30 30-40 40-50
Frequency 12 28 32 25 13
Solution: Class (CI) Frequency
(fi)
Class mark
(xi)
di = xi – a fidi
0-10 12 5 5 – 25 = – 20 -240
10-20 28 15 15 – 25 = –10 -280
20-30 32 25 = a 25-25 = 0 0
30-40 25 35 35-25 = 10 250
40-50 13 45 45-25 = 20 260
Total Σfi =110 Σfidi = -10
Assumed mean = a = 25
Mean of the data:
= 25 + (-10/ 110)
= 25 -( 1/11)
= (275-1)/11
= 274/11
=24.9
Hence, the mean marks of the
students are 24.9.

9. Continuous Distribution Method

10. Median
• Median is the middle value of the set of data when ranked according to
the size either ascending or descending numerical order.
• Median value can then be calculated using the following formula:
Median= (N+1)/2
Odd number of observations
Median = {(n+1)/2}thterm
Even number of observations
Where,
‘n’ is the number of
observations in all
the cases.

11. Median for Discrete Series
We can find median using following steps:-
i. Calculate the cumulative frequencies
ii. Find (N+1)/2, where N=Σf=total frequencies
iii. Identify the cumulative frequency just greater than (N+1)/2
iv. The value of x corresponding to that cumulative frequency is
the (N+1)/2 median

12. Example:
The following data are the weights of students in a class. Find the median weights of
the students.
Solution:
The cumulative frequency greater
than 30.5 is 38.
The value of x corresponding to
38 is 40.
The median weight of the
students is 40 kgs.

13. Median for Continuous Series
Where,
• l = Lower limit of the median class
• N = Total Numbers of frequencies
• f = Frequency of the median class
• m = Cumulative frequency of the class preceding the median class
• c = the class interval of the median class.

14. Example:
The following data attained from a garden records of certain period Calculate the
median weight of the apple.
Solution:

15. Mode
• Mode is defined as the value which occurs most frequently in a data set.
• The mode obtained may be two or more in frequency distribution.
Types of Mode:-
• Unimodal-
- 6.3, 4.9, 8.9, 6.3, 4.9, 4.9
4.9 is mode
• Bi-modal
-21, 28, 28, 41, 43, 43
28 and 43 both are mode here.

16. Mode for Ungrouped Data
Example
The following are the marks scored by 20 students in the class.
Find the mode 90, 70, 50, 30, 40, 86, 65, 73, 68, 90, 90, 10, 73, 25, 35, 88, 67, 80, 74, 46
Since the marks 90 occurs the maximum number of times, three times compared with the
other numbers, mode is 90.
Solution:
Example
Calculate the mode from the following data
Solution:
Here, 7 is the maximum frequency, hence the value of x corresponding to 7 is 8.
Therefore 8 is the mode.

17. Mode By Continuous Grouped Method
Modal class is the class which has maximum frequency.
Where,
f1 = frequency of the modal class
f0 = frequency of the class preceding the modal class
f2 = frequency of the class succeeding the modal class
c = width of the class limits

18. Example
Find the mode from the following table using grouping method
Mode By Continuous Grouped Method

19. Solution:

20. It can be seen from the above table, that the maximum frequency
occurs 5-5 times in both class-intervals (40-50) and (50-60).

21. Thus, to determine the mode class between the two,
we’ll have to carry out a density test:-

22. Thank You