Question 712177
I'll do part a) and let you do part b)


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

63,75,80,80,80,80,82,90,92,92


Sample 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 10).

{{{Mean=(63+75+80+80+80+80+82+90+92+92)/10=814/10=81.4}}}


So the mean is 81.4


----------------------------------------------------------------

Median:



To find the median, count off about 5 spaces (just take half of the size of the list, which is 10) from the beginning of the list until you hit the middle. Now count count off about 5 spaces from the end of the list until you hit the middle.

63, 75, 80, 80, {{{highlight(80)}}}, {{{highlight(80)}}}, 82, 90, 92, 92

Since the middle is in between the numbers 80 and 80, add them up and divide that sum by 2.

{{{Median=(80+80)/2=160/2=80}}}


So the median is 80


----------------------------------------------------------------

Mode:


To find the mode, simply look for any repeating numbers. If there is one number that occurs more frequently than any other number, then that number is the mode.

Since 80 repeats itself 4 times (which is more frequent than any other number), the mode is 80



So the mode is 80


---------------------------------------------------------------------------------------------------------


Sample Standard Deviation (i.e. take a random sample of population and not measure whole population):



Use this formula to find the Sample standard deviation:


Sample 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 10


*[Tex \LARGE\sqrt{ \frac{1}{10-1}\displaystyle\sum_{i=0}^{10} (x_i-\bar{x})^2}]


Subtract {{{10-1}}} to get 9


*[Tex \LARGE\sqrt{ \frac{1}{9}\displaystyle\sum_{i=0}^{10} (x_i-\bar{x})^2}]


Replace  *[Tex \LARGE \bar{x}] with 81.4


*[Tex \LARGE\sqrt{ \frac{1}{9}\displaystyle\sum_{i=0}^{10} (x_i-81.4)^2}]


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



{{{sqrt((1/9)((63-81.4)^2+(75-81.4)^2+(80-81.4)^2+(80-81.4)^2+(80-81.4)^2+(80-81.4)^2+(82-81.4)^2+(90-81.4)^2+(92-81.4)^2+(92-81.4)^2))}}}


Subtract the terms in the parenthesis


{{{sqrt((1/9)((-18.4)^2+(-6.4)^2+(-1.4)^2+(-1.4)^2+(-1.4)^2+(-1.4)^2+(0.6)^2+(8.6)^2+(10.6)^2+(10.6)^2))}}}


Square each term


{{{sqrt((1/9)(338.56+40.96+1.96+1.96+1.96+1.96+0.36+73.96+112.36+112.36))}}}


Add up all of the terms


{{{sqrt((1/9)686.4)}}}


Multiply


{{{sqrt(76.2666666666667)}}}


Take the square root


{{{8.73307887670017}}}


So the sample standard deviation is {{{8.73307887670017}}}