Question 89006
First lets find the mean:


To find the mean, add up all of the numbers and divide the sum by the number of numbers (which in this case is 3).

{{{Mean=(88.7+ 91.2+ 94.6 )/3=274.5/3=91.5}}}


So the mean is 91.5



Use this formula to find the standard deviation:


Standard Deviation:*[Tex \LARGE  \sigma=\sqrt{ \frac{1}{N}\displaystyle\sum_{i=0}^N (x_i-\bar{x})^2}] where *[Tex \LARGE \bar{x}] is the mean, *[Tex \LARGE x_i] is the ith number, and *[Tex \LARGE N] is the number of numbers




So we can replace N with 3


*[Tex \LARGE\sqrt{ \frac{1}{3}\displaystyle\sum_{i=0}^3 (x_i-\bar{x})^2}]


Replace  *[Tex \LARGE \bar{x}] with 91.5


*[Tex \LARGE\sqrt{ \frac{1}{3}\displaystyle\sum_{i=0}^3 (x_i-91.5)^2}]


Expand the summation (replace each {{{x[i]}}} with the respective number)



{{{sqrt((1/3)((88.7-91.5)^2+( 91.2-91.5)^2+( 94.6 -91.5)^2))}}}


Subtract the terms in the parenthesis


{{{sqrt((1/3)((-2.8)^2+(-0.3)^2+(3.1)^2))}}}


Square each term


{{{sqrt((1/3)(7.84+0.09+9.61))}}}


Add up all of the terms


{{{sqrt((1/3)17.54)}}}


Multiply


{{{sqrt(5.84666666666667)}}}  


Take the square root


{{{2.41798814444295}}}


So the standard deviation is {{{2.41798814444295}}}


So if you round to the nearest hundredth, you get 2.42. So the answer is C)