Download STATISTIC05 Dispersion

STATISTICS
“CALCULATING DESCRIPTIVE
STATISTICS –Measures of
Dispersion”
4.0 Measures of Dispersion
3.0 Measures of Dispersion
• Measures of Dispersion
– Describe how far individual data values have strayed
from the mean (average)
– The ways to measure the dispersion of our data are
range, variance (sample & population) and standard of
deviation.
3.0 Measures of Dispersion
RANGE
1.
The simplest measure of dispersion and is
calculated by the difference between the highest
value and the lowest value in the data set.
2.
The range of a sample is obtained by subtracting
the smallest measurement from the largest
measurement
3.0 Measures of Dispersion
VARIANCE
1.
One of the most common measurement of dispersion in
statistics
2.
Summarize the squared deviation of each data value from
the mean.
3.
The variance describes the relative distance between the
data points in the sets and the mean of the set.
3.0 Measures of Dispersion
Variance
N
n
σ² =
∑(x
i -x
)
= the size of the population
σ² = the variance of the population
2
Xi
i =1
= the values in the sample; X1 = first
data, X2 = second data
n
(xi
x
= the sample mean
-x
) = the deviation from the mean for each
value in the data set
3.0 Measures of Dispersion
Variance (Group Data)
m
m
n
σ² =
∑(x
i -x
)
2
= the number of classes
σ² = the variance of the Group data
fi
Xi
i =1
= the values in the sample; X1 = first
data, X2 = second data
fi
(xi
x
= the sample mean
-x
) = the deviation from the mean for each
value in the data set
n = the total number of values in the data set
3.0 Measures of Dispersion
STANDARD DEVIATION
1.
Very straightforward and clear
2.
A standard deviation is the square root of
variance.
3.
Describe the actual and useful measure since the
standard deviation is in the units of the original
data sets
3.0 Measures of Dispersion
Std Deviation (Sample)
n
n
√
S =
∑ (x
i -x
)
= the size of the sample
S² = the variance of the sample
2
Xi
i =1
= the values in the sample; X1 = first
data, X2 = second data
n
(xi
x
= the sample mean
-x
) = the deviation from the mean for each
value in the data set
3.0 Measures of Dispersion
Std Deviation (Group Data)
m
m
n
√
s =
∑
(xi
-x
)
2
= the number of classes
σ² = the variance of the Group data
fi
Xi
i =1
= the values in the sample; X1 = first
data, X2 = second data
fi
(xi
x
= the sample mean
-x
) = the deviation from the mean for each
value in the data set
f = the total number of values in the data set
3.0 Measures of Relative Position
Measures of Relative Position
1. Describe the percentage of the data
below a certain point.
2. The technique to measure relative position
is Quartiles and Interquartile Range
3.0 Measures of Relative Position
QUARTILES
1.
Divide the data set into 4 equal segments after it
has been arranged in ascending order.
2.
25% data points = first quartile Q (Mean data below median)
50% data points = second quartile Q (Median)
75% data points = third quartile Q (Mean data after median)
1
2
3
3.0 Measures of Relative Position
INTERQUARTILE RANGE
1. Simple the difference between the third
and first quartiles.
IQR = Q3 –Q1
2. The interquartile range measures the
spread of the center half of the data set.
3.0 Measures of Relative Position
INTERQUARTILE RANGE
3. Use to identify outliers, which are
extreme values that should be
discarded before analysis
Q1 - 1.5(IQR) > Outliers (Discarded) > Q3 + 1.5(IQR)
Try This!
Table below indicates a survey that MAS carried out on 50
consumer base on the number of flight hours they are
willing to travel. Calculate the mean, median, mode,
variance and Standard deviation of the table below.
Hours
10
15
20
25
30
35
40
14
19
24
29
34
39
44
Number of passengers
12
9
6
9
6
6
2
50
Try This
The following frequency distribution indicates the daily
number of foreigner from European region landed on
Malaysia using MAS in 50 days.
Classes
10
17
24
31
38
45
52
59
16
23
30
37
44
51
58
65
Freq
8
11
5
6
7
5
7
1
50
Calculate the RFD, CFD, mean, median, mode, variance
and standard deviation of the data above
QUIZ 2
The scores of Statistics Examination (100%) is as follows:
30
61
99
29
98
48
56
77
85
35
67
88
43
100
55
25
39
43
62
68
33
52
66
73
80
45
89
74
93
75
a) Construct a frequency distribution with 6/7/8 classes:
b) Construct a relative and a cumulative FD from the data a)
c) Calculate the mean, median,mode, variance and Std. Deviation
of the passengers
d) The all the results obtained in a,b and c, describe statistically in your
own words your own observation of scores
QUIZ 3
The scores of Statistics Examination (100%) is as follows:
30
61
99
29
98
48
56
77
85
35
67
88
43
100
55
25
39
43
62
68
33
52
66
73
80
45
89
74
93
75
a) Construct a frequency distribution with 8 class
b) Calculate the the Q1, Q2 and Q3
c) Calculate the IQR and Outliers (Discarded) data
d) Describe in your own words, the validity of the outliers