Question 1102937
Find the center point for each bin, as an example,
{{{C[1]=(91+100)/2=95.5}}}
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{{{95.5}}},{{{3}}}
{{{85.5}}},{{{4}}}
{{{75.5}}},{{{8}}}
{{{65.5}}},{{{4}}}
{{{55.5}}},{{{3}}}
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To find the mean, find the weighted average,
{{{mu= (95.5*3+85.5*4+75.5*8+65.5*4+55.5*3)/(3+4+8+4+3) = 75.5}}}
You could have also used a symmetry argument since the data values are centered about 75.5.
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Now for the standard deviation, sum the deviations from the mean, weight them, and take the square root.
{{{ sigma^2=((95.5-75.5)^2*3+(85.5-75.5)^2*4+(75.5-75.5)^2*8+(65.5-75.5)^2*4+(55.5-75.5)^2*3)/22}}}
{{{ sigma^2=145.4545}}}
{{{sigma=12.1}}}