calculating mean in a discrete series by step deviation
to calculate median?
Answers
Answer:
good morning sir yes sir I
Answer:
When data is given alongwith their frequencies. Following is an example of discrete series:
Items 5 10 20 30 40 50 60 70
Frequency 2 5 1 3 12 0 5 7
For discrete series, the Mean Deviation can be calculated using the following formula.
Formula
MD=∑f|x−Me|N=∑f|D|N
Where −
N = Number of observations.
f = Different values of frequency f.
x = Different values of items.
Me = Median.
The Coefficient of Mean Deviation can be calculated using the following formula.
Coefficient of MD=MDMe
Example
Problem Statement:
Calculate Mean Deviation and Coefficient of Mean Deviation for the following discrete data:
Items 14 36 45 50 70
Frequency 2 5 1 1 3
Solution:
Based on the given data, we have:
xi Frequency
fi fixi |xi−Me| fi|xi−Me|
14 2 28 31 62
36 5 180 9 45
45 1 45 0 0
50 1 50 5 5
70 3 210 15 45
N=12 ∑fi|xi−Me|=157
Median
Me=(N+12)th Item=(62)th Item=3rd Item=45
Based on the above mentioned formula, Mean Deviation MD will be:
MD=∑f|D|N=15712=13.08
and, Coefficient of Mean Deviation MD will be:
=MDMe=13.0845=0.29
The Mean Deviation of the given numbers is 13.08.
The coefficient of mean deviation of the given numbers is 0.29.