#1**0 **

As of further review, my solution is wrong, so I'll just delete this garble that I wrote...

TheXSquaredFactor
May 20, 2017

edited by
Guest
May 21, 2017

#3**0 **

You have calculated the Mean Absolute Deviation Guest #1, not the standard deviation!

.

Alan
May 21, 2017

#5**0 **

I guess I should take my solution down then because my solution is wrong...

I feel bad for giving a user incorrect info...

TheXSquaredFactor
May 21, 2017

#2**+1 **

Find the (sample) standard deviation of the list:

(89, 93, 92, 88, 89, 87, 95, 94, 91, 92)

The standard deviation is given by:

sqrt((variance))

The (sample) variance of a list of numbers X = {X_1, X_2, ..., X_n} with mean μ = (X_1 + X_2 + ... + X_n)/n is given by:

(abs(X_1 - μ)^2 + abs(X_2 - μ)^2 + ... + abs(X_n - μ)^2)/(n - 1)

There are n = 10 elements in the list X = {89, 93, 92, 88, 89, 87, 95, 94, 91, 92}:

(abs(X_1 - μ)^2 + abs(X_2 - μ)^2 + abs(X_3 - μ)^2 + abs(X_4 - μ)^2 + abs(X_5 - μ)^2 + abs(X_6 - μ)^2 + abs(X_7 - μ)^2 + abs(X_8 - μ)^2 + abs(X_9 - μ)^2 + abs(X_10 - μ)^2)/(10 - 1)

The elements X_i of the list X = {89, 93, 92, 88, 89, 87, 95, 94, 91, 92} are:

X_1 = 89

X_2 = 93

X_3 = 92

X_4 = 88

X_5 = 89

X_6 = 87

X_7 = 95

X_8 = 94

X_9 = 91

X_10 = 92

(abs(89 - μ)^2 + abs(93 - μ)^2 + abs(92 - μ)^2 + abs(88 - μ)^2 + abs(89 - μ)^2 + abs(87 - μ)^2 + abs(95 - μ)^2 + abs(94 - μ)^2 + abs(91 - μ)^2 + abs(92 - μ)^2)/(10 - 1)

The mean (μ) is given by

μ = (X_1 + X_2 + X_3 + X_4 + X_5 + X_6 + X_7 + X_8 + X_9 + X_10)/10 = (89 + 93 + 92 + 88 + 89 + 87 + 95 + 94 + 91 + 92)/10 = 91:

(abs(89 - 91)^2 + abs(93 - 91)^2 + abs(92 - 91)^2 + abs(88 - 91)^2 + abs(89 - 91)^2 + abs(87 - 91)^2 + abs(95 - 91)^2 + abs(94 - 91)^2 + abs(91 - 91)^2 + abs(92 - 91)^2)/(10 - 1)

The values of the differences are:

89 - 91 = -2

93 - 91 = 2

92 - 91 = 1

88 - 91 = -3

89 - 91 = -2

87 - 91 = -4

95 - 91 = 4

94 - 91 = 3

91 - 91 = 0

92 - 91 = 1

10 - 1 = 9

(abs(-2)^2 + abs(2)^2 + abs(1)^2 + abs(-3)^2 + abs(-2)^2 + abs(-4)^2 + abs(4)^2 + abs(3)^2 + abs(0)^2 + abs(1)^2)/9

The values of the terms in the numerator are:

abs(-2)^2 = 4

abs(2)^2 = 4

abs(1)^2 = 1

abs(-3)^2 = 9

abs(-2)^2 = 4

abs(-4)^2 = 16

abs(4)^2 = 16

abs(3)^2 = 9

abs(0)^2 = 0

abs(1)^2 = 1

(4 + 4 + 1 + 9 + 4 + 16 + 16 + 9 + 0 + 1)/9

4 + 4 + 1 + 9 + 4 + 16 + 16 + 9 + 0 + 1 = 64:

64/9

The standard deviation is given by

sqrt((variance)) = sqrt(64/9) = 8/3:

**Answer: | 8/3**

Guest May 20, 2017