Question

individual series standard deviation ​

Answer 1

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.