Question 202195
First sort the numbers into ascending order (from least to greatest):

0.202,0.349,0.365,0.426,0.427,0.569,0.669



Now let's find the mean. So add up all of the numbers and divide the sum by the number of numbers (which in this case is 7).

{{{Mean=(0.202+0.349+0.365+0.426+0.427+0.569+0.669)/7=3.007/7=0.42957}}}


So the mean is 0.42957




Use this formula to find the Standard Deviation:


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


So we can replace N with 7


*[Tex \LARGE\sqrt{ \frac{1}{7-1}\displaystyle\sum_{i=0}^7 (x_i-\bar{x})^2}]


Subtract {{{7-1}}} to get 6


*[Tex \LARGE\sqrt{ \frac{1}{6}\displaystyle\sum_{i=0}^7 (x_i-\bar{x})^2}]


Replace  *[Tex \LARGE \bar{x}] with 0.42957


*[Tex \LARGE\sqrt{ \frac{1}{6}\displaystyle\sum_{i=0}^7 (x_i-0.42957)^2}]


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



{{{sqrt((1/6)((0.202-0.42957)^2+(0.349-0.42957)^2+(0.365-0.42957)^2+(0.426-0.42957)^2+(0.427-0.42957)^2+(0.569-0.42957)^2+(0.669-0.42957)^2))}}}


Subtract the terms in the parenthesis


{{{sqrt((1/6)((-0.228)^2+(-0.081)^2+(-0.065)^2+(-0.004)^2+(-0.003)^2+(0.139)^2+(0.239)^2))}}}


Square each term


{{{sqrt((1/6)(0.051984+0.006561+0.004225+0.000016+0.000009+0.019321+0.057121))}}}


Add up all of the terms


{{{sqrt((1/6)0.139237)}}}


Multiply


{{{sqrt(0.0232061666666667)}}}


Take the square root


{{{0.152335703847347}}}


So the standard deviation is {{{0.152335703847347}}}



which rounds to 0.1523



So the answer is D) 0.1523