How can I find the sample mean and the standard deviation?

Question

75
74
80
68
79
85
77
82
79
67
90
72
76
75
69
85
78
79
82
66
75
85
90
76
85
67
89
82
69
79
82
80
84
79
78
81
77
84
80
76
How can I find the sample mean and the sample standard deviation of the amount citizens spend in a year. The average amount people spend per year is 75 dlls.

Answer 1

To find the sample mean simply add up all the scores and divide by the amount of scores (n). To find the standard deviation, subtract n from each score, and then divide by (n-1). Next square root this and you're ready to go!



~*Wintergreen*~

Answer 2

to find the mean, you add up all the numbers and divide by how many numbers there are.



The standard deviation measures the spread of the data about the mean value. It is useful in comparing sets of data which may have the same mean but a different range. For example, the mean of the following two is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. However, the second is clearly more spread out. If a set has a low standard deviation, the values are not spread out too much.



Example:

Find the standard deviation of 4, 9, 11, 12, 17, 5, 8, 12, 14

First work out the mean: 10.222

Now, subtract the mean individually from each of the numbers in the question and square the result. This is equivalent to the (x - xbar)² step. x refers to the values in the question.



x 4 9 11 12 17 5 8 12 14

(x - x)² 38.7 1.49 0.60 3.16 45.9 27.3 4.94 3.16 14.3



Now add up these results (this is the 'sigma' in the formula): 139.55

Divide by n-1. n is the number of values, so in this case is 8: 17.44

And finally, square root this: 4.18

Answer 3

mean = 28.714. Standard deviation = 9.361.

Answer 4

mean is the average or



sum of entries / (number of entries)



Sample Deviation =

Sqr Rt of ((sum of (entry - mean)^2)/(no. of entries -1))