Transcript S1.2 Calculating means and standard deviations

AS-Level Maths:
Statistics 1
for Edexcel
S1.2 Calculating means
and standard deviations
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Contents
Standard deviation
Calculating means
Calculating standard deviations
Coding
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Standard deviation
There are three commonly used measures of spread (or
dispersion) – the range, the inter-quartile range and the
standard deviation.
The standard deviation is widely used in statistics to measure
spread. It is based on all the values in the data, so it is
sensitive to the presence of outliers in the data.
The variance is related to the standard deviation:
variance = (standard deviation)2
The following formulae can be used to find the variance and s.d.
(x  x )

variance 
i
n
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2
s.d. 
 (x  x )
2
i
n
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Standard deviation
Example: The mid-day temperatures (in °C) recorded for
one week in June were: 21, 23, 24, 19, 19, 20, 21
First we find the mean: x 
xi
xi  x
( xi  x )2
21
0
0
23
2
4
24
3
9
19
-2
4
19
-2
4
20
-1
1
21
0
0
Total:
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21 23  ...  21 147

 21°C
7
7
(x  x )

variance 
2
i
n
So variance = 22 ÷ 7 = 3.143
So, s.d. = 1.77°C (3 s.f.)
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