You can
put this solution on YOUR website! 6. Using the following distribution of scores and the
standard deviation formula of:
s = √∑(x-mean)˛/(n-1)
where: s = standard deviation
x = individual’s score
n = number of scores
fill in the missing values (worth 70 points):
_ _
score deviation = (x – x) (x – x)˛
student 1: 55 __________________ _______
student 2: 60 __________________ _______
student 3: 62 __________________ _______
student 4: 43 __________________ _______
student 5: 100 __________________ _______
student 6: 90 __________________ _______
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∑x = ____
n = ____
_
mean = x = _____
standard deviation = _____
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Add the scores and get ∑x = 410
Count the scores and get n = 6
_
Divide 410 by 6 and get mean = x = 68.33333333
Subtract this from each score to get the deviations
_
x - x
55 - 68.33333333 = -13.33333333
60 - 68.33333333 = -8.33333333
62 - 68.33333333 = -6.33333333
43 - 68.33333333 = -25.33333333
100 - 68.33333333 = 31.66666667
90 - 68.33333333 = 21.66666667
_
Square each of those to get (x - x)˛
(-13.33333333)˛ = 177.7777778
(-8.33333333)˛ = 69.4444444
(-6.33333333)˛ = 40.1111111
(-25.33333333)˛ = 641.7777778
(31.66666667)˛ = 1002.7777778
(21.66666667)˛ = 469.4444444
_
Add those to get ∑(x - x)˛ = 2401.333333
Divide by n-1, that is, by 6-1 which is 5
Divide by 5 and that's the variance, s˛ = 480.2666667
Take the square root of the variance to find
standard deviation = s = 21.91498726
Edwin
