Find the standard deviation of {7, 13, 15, 11, 4}

Given:

7, 13, 15, 11, 4

Formula used:

 \({\rm{S}}.{\rm{D}} = √ {\frac{{∑|{\rm{x}} - {\rm{\;m|^2}}}}{{\rm{n}}}} \)

Mean (m) = Total of observations/number of observations

S.D = standard deviation

∑ = summation

x = observation

m = mean of the observations

n = number of observation

Calculation:

Mean of 7, 13, 15, 11, 4

⇒ 50/5

⇒ 10

\({\rm{S}}.{\rm{D}} = √ {\frac{{{{\left( {7 - 10} \right)}^2} + {{\left( {13 - 10} \right)}^2} + {{\left( {15\; - \;10} \right)}^2} + {{\left( {11 - 10} \right)}^2} + \;{{\left( {4 - 10} \right)}^2}}}{5}} \)

⇒ \(√ {\frac{{9 + \;9 + 25 + 1 + 36}}{5}} \)

⇒ \(√ {\frac{{80}}{5}} \)

⇒ √16

⇒ 4

∴ The standard deviation is 4