individual series standard deviation
Answers
Answer:
When data is given on individual basis. Following is an example of individual series:
Items 5 10 20 30 40 50 60 70
For individual series, the Standard Deviation can be calculated using the following formula.
Formula
σ=∑ni=1(x−x¯)2N−1−−−−−−−−√
Where −
x = individual observation of variable.
x¯ = Mean of all observations of the variable
N = Number of observations
Example
Problem Statement:
Calculate Standard Deviation for the following individual data:
Items 14 36 45 70 105
Solution:
X x¯ x−x¯ (x−x¯)2
14 54 -40 1600
36 54 -18 324
45 54 -9 81
70 54 16 256
105 54 51 2601
N=5 ∑(x−x¯)2=4862
Based on the above mentioned formula, Standard Deviation σ will be:
σ=∑(x−x¯)2N−1−−−−−−−√=48624−−−−√=48624−−−−√=34.86
The Standard Deviation of the given numbers is 34.86.