ST1381 ELEMENTARY STATISTICS

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There are three basic operational rules which help to simplify the use of the sigma notation.
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1. For any integer N
Operational Rules for
Summation
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N
i i N i i
N
i i i y x y x
1
1
1
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2. If c is a constant, that is, does not depend on the index of summation i, then
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Nc c and x c cx N i N i i
N
i i 
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1
1
1
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The graphical representation of data gives us the idea on the shape of the distribution (population).
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The mean, median and mode which we shall define in this section provide estimates for the centre of the distribution DEFINITION OF THE
MEASURES OF LOCATION
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The
mean ( or the arithmetic mean, to give its full title) can be defined as the value which each item in the distribution would have if all the values were shared out equally among the items.
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For instance, if three people had M2, M3 and M7 respectively, the mean amount would be M4, i.e.
M12 shared equally between the three people.
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7
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2
16
4
45
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2
5
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0
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8
8
8
45
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2 mod 
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 e x
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The median for grouped data is calculated using the following formula
Where l = the lower class boundary of the median class, n = total frequency,
F = the cumulative frequency of the previous class, f = the frequency of the median class and w = the class width
Median
w f F n l x median
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2
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 i Class
Class Mark, x i Frequency, f i Cumulative
Frequency
1
2
3
4
5
1.5
–
1.9
2.0
–
2.4
2.5
–
2.9
3.0
–
3.4
3.5
–
3.9
4.0
-
4.4
1.7
2.2
2.7
3.2
3.7
4.2
3
10
18
10
7
2
3
13
31
41
48
50
Total
50
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7833
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2
3333
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0
45
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2
)
5
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0
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6667
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0
(
45
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2
5
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0
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18
13
2
50
45
.
2
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 median x
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A measure of variation is a way of indicating how dispersed a set of observations is.
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