SOLUTION: Hello, please help with this question. I'm stuck The lengths, in inches, of a sample of eight Brazilian Barking Treefish are given below.11, 17, 24, 26, 27, 29, 34, 42 Round the

Algebra ->  Probability-and-statistics -> SOLUTION: Hello, please help with this question. I'm stuck The lengths, in inches, of a sample of eight Brazilian Barking Treefish are given below.11, 17, 24, 26, 27, 29, 34, 42 Round the      Log On


   

Question 734489: Hello, please help with this question. I'm stuck
The lengths, in inches, of a sample of eight Brazilian Barking Treefish are given below.11, 17, 24, 26, 27, 29, 34, 42 Round the following to 2 DECIMAL PLACES if necessary.
Find the sample mean weight.
Find the sample standard deviation.
Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
The sample mean is the average and is computed as the sum of all the observed outcomes from the sample divided by the total number of events.

mean=%2811%2B17%2B24%2B+26%2B27%2B29%2B34%2B42%29%2F8

mean=210%2F8

mean=26.25

Variance and Standard Deviation: Step by Step
Calculate the mean,+x.

x=26.25
Write a table that subtracts the mean from each observed value.
x+------- x+-+26.25------- %28x+-+26.25+%29%5E2+
11-------+-15.25------- 232.5625
17 ------- +-9.25------- 85.5625
24------- +-2.25------- 5.0625
26------- +-0.25------- 0.0625
27------- +0.75------- 0.5625
29------- +2.75------- 7.5625
34------- +7.75------- 60.0625
42------- +15.75------- 248.0625


Total:

Divide 639.5 by n+-1 where n=8 is the number of items in the sample.
639.5%2F8=79.9375 This is the variance.
To get the standard deviation we take the square root of the variance.
sqrt%2879.9375%29=8.94


Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
In this case the sample mean weight is the same as the average, that is, all Treefish contribute equally to the average so
11 + 17 + 24 + 26 + 27 +29 + 34 + 42 divided by the population size (8) is 26.25 inches
the sample standard deviation is calculated by summing the square of the differences between the population members and the sample mean weight and dividing that sum by 8 - 1 or 7, then take the square root of that result.....the formula for sample standard deviation is
square root of summation ((X - X mean) squared / N -1) where N is population size
the calculation is
(11-26.25)^2 + (17-26.25)^2 + 26-26.25)^2 + 27-26.25)^2 + (29-26.25)^2 + (34-26.25)^2 + (42-26.25)^2 + (24-26.25)^2 = 232.56 + 85.56 + .06 + .56 + 7.56 + 60.06 + 248.06 + 5.06 = 639.48 / 7 = 91.35
now we take the square root of 91.35 = 9.56 which is the sample standard deviation