Question

standard deviation for continous frequency table
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Answer 1

Answer:

When data is given based on ranges alongwith their frequencies. Following is an example of continous series:

Items 0-5 5-10 10-20 20-30 30-40

Frequency 2 5 1 3 12

In case of continous series, a mid point is computed as lower−limit+upper−limit2 and Standard deviation is computed using following formula.

Formula

σ=∑ni=1fi(xi−x¯)2N−−−−−−−−−−√

Where −

N = Number of observations = ∑f.

fi = Different values of frequency f.

xi = Different values of mid points for ranges.

x¯ = Mean of mid points for ranges.

Example

Problem Statement:

Let's calculate Standard Deviation for the following continous data:

Items 0-10 10-20 20-30 30-40

Frequency 2 1 1 3

Solution:

Based on the given data, we have:

Mean

x¯=5×2+15×1+25×1+35×37=10+15+25+1057=22.15

Items Mid-pt

x Frequency

f x¯ x−x¯ f(x−x¯)2

0-10 5 2 22.15 -17.15 580.25

10-20 15 1 22.15 -7.15 51.12

20-30 25 1 22.15 2.85 8.12

30-40 35 3 22.15 12.85 495.36

N=7 ∑f(x−x¯)2=1134.85

Based on the above mentioned formula, Standard Deviation σ will be:

σ=∑ni=1fi(xi−x¯)2N−−−−−−−−−−√=1134.857−−−−−√=12.73

The Standard Deviation of the given numbers is 12.73.