Question 1187619


 

calculate the variance of the follow data set: {{{60g}}}, {{{56g, {{{61g}}}, {{{68g}}}, {{{51g}}}, {{{53g}}}, {{{69g}}},{{{ 54g}}}

{{{variance=sqrt((x[i]-mu)^2/(n-1))}}}

The first step is to calculate the mean. 

mean {{{mu= (60+56+61+68 +51+53 +69 +54)/8=472/8=59}}}

Then you take each value in data set, subtract the mean and square the difference. For instance, for the first value:

{{{(60 - 59)^2  = 1}}}
{{{(56 - 59)^2  = 9}}}
{{{(61 - 59)^2  =4}}}
{{{(68 - 59)^2  =81}}}
{{{(51 - 59)^2=64}}}
{{{(53 - 59)^2=36}}}
{{{(69 - 59)^2=100}}}
{{{(54 - 59)^2=25}}}

The squared differences for all values are added:

{{{1+ 9+ 4 + 81 + 64+36+100+25 = 320}}}

plug it in formula

{{{variance=320/(8-1) = 320/7=45.71}}}