Find the standard deviation for the following data :

Explanation

We have
`"Mean, "barx=(Sigmaf_(i)x_(i))/(Sigmaf_(i))=((18+80+182+180+230))/(50)=(690)/(50)=13.8.`
This value being in decimal form, the calculation will become tedious.
So, we use the formula, `sigma=(1)/(N)cdotsqrt(Ncdot Sigmaf_(i)x_(i)^(2)-(Sigmaf_(i))^(2)).`
Now, we prepare the table given below :

`therefore" "N=Sigmaf_(i)=50, Sigmaf_(i)x_(i)=690 and Sigmaf_(i)x_(i)^(2)=11590`
`therefore" standard deviation, "sigma=(1)/(N)cdot{sqrt(Ncdot Sigmaf_(i)x_(i)^(2)-(Sigmaf_(i)x_(i))^(2))}`
`rArr" "sigma=(1)/(50)cdot sqrt(50xx11590-(690)^(2))=(1)/(50)xxsqrt(579500-(690)^(2))`
`=(1)/(50)sqrt(579500-476100)=(1)/(50)xxsqrt(103400)=(321.5)/(50)=6.43.`
Hence, `sigma=6.43.`