# Standard deviation

Find standard deviation for dataset (grouped data):

Age (years) No. Of Persons
0-10 15
10-20 15
20-30 23
30-40 22
40-50 25
50-60 10
60-70 5
70-80 10

Result

s =  19.758

#### Solution:

$n=15+15+23+22+25+10+5+10=125 \ \\ \ \\ m_{ 1 }=5 \cdot \ 15+15 \cdot \ 15+25 \cdot \ 23+35 \cdot \ 22+45 \cdot \ 25+55 \cdot \ 10+65 \cdot \ 5+75 \cdot \ 10=4395 \ \\ m=m_{ 1 }/n=4395/125=\dfrac{ 879 }{ 25 }=35.16 \ \\ \ \\ s_{ 1 }=5^2 \cdot \ 15+15^2 \cdot \ 15+25^2 \cdot \ 23+35^2 \cdot \ 22+45^2 \cdot \ 25+55^2 \cdot \ 10+65^2 \cdot \ 5+75^2 \cdot \ 10=203325 \ \\ \ \\ s_{ 2 }=s_{ 1 }/n - m^2=203325/125 - 35.16^2=390.3744 \ \\ \ \\ s=\sqrt{ s_{ 2 } }=\sqrt{ 390.3744 } \doteq 19.7579 \doteq 19.758$

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Dr Math
Check also with our stddev calculator - input is given as frequency table:

https://www.hackmath.net/en/calculator/standard-deviation?input=5+15+25+35+45+55+65+75%0D%0Af%3A15+15+23+22+25+10+5+10

x is Mid Interval Value and f is frequency

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