Do you want to learn " How to calculate standard deviation in 6 easy steps"!! click here...
Do you want to learn " How to calculate standard deviation in 6 easy steps"!! click here
...
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Before we jump on to the calculations, let's find out what standard deviation is ! well it's...
Before we jump on to the calculations, let's find out what standard deviation is ! well it's...
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"A quantity expressing by how much the members of a group differ from the mean value for the group"
"A quantity expressing by how much the members of a group differ from the mean value for the group"
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Standard deviation is useful in assessing risk factors and investment options.
Standard deviation is useful in assessing risk factors and investment options.
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formula used to calculate standard deviation is:
σ=√1N∑Ni=1(Xi−μ)2. where...
formula used to calculate standard deviation is:
σ=√1N∑Ni=1(Xi−μ)2. where...
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μ = Assumed mean
σ= Population standard deviation
now let's move on to steps to solve with an example's help....
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6
40
60
52
32
65
1
2
3
4
5
Assume a data set of 6 scores:
41
find the mean.
find each scores deviation from mean.
square each deviation from mean.
1
2
3
steps
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find the square root of the variance.
find the sum of squares.
.
find the variance.
4
5
6
steps
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find the mean as follows:
step 1
(40+60+32+65+52+41)/6=48.33. so,
mean=48.33
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find each
scores deviation from mean:
40-48.33=-8.33
60-48.33=11.76
32-48.33=-16.33
65-48.33=16.67
52-48.33=3.67
41-48.33=-7.33
step 2
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square each deviation from mean
:
step 3
(-8.33)*2 = 69.38
(11.76)*2 = 138.2
(-16.33)*2= 266.6
(16.67)*2 =277.8
(3.67)*2 = 13.46
(-7.33)*2 =53.72
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find the sum of squares (this is called sum of squares):
step 4
(69.38+138.2+266.6+277.8+13.46+53.72) = 719.14
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find the variance:
( divide the sum of the squares by N (FOR POPULATION) and (n-1 for sample).
step 5
POPULATION:
719.14 /6=119.8
SAMPLE:
719.14 /(6-1) =
143.82
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find the square root of the variance.
.
step 6
POPULATION:
√
119.8 =
10.94
SAMPLE:
√ 143.82 = 11.99
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from these calculations
we can say that each score deviates from the mean by 10.94 for population and 11.99 for sample.
1
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