Transcript Lecture-2: Descriptive Statistics: Measures of Location

WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful Islam
WFM 5201: Data Management and
Statistical Analysis
Lecture-2: Descriptive Statistics
[Measures of Location]
Akm Saiful Islam
Institute of Water and Flood Management (IWFM)
Bangladesh University of Engineering and Technology (BUET)
April, 2008
WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful Islam
Descriptive Statistics
Measures of Central Tendency
 Measures of Location
 Measures of Dispersion
 Measures of Symmetry
 Measures of Peakdness

WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful Islam
Measures of Location

Measures that are allied to the median include
the quartiles, deciles and percentiles, because
they are also based on their position in a series
of observations.

These measures are referred to as measures of
location and not the measures of central
tendency as they describe the position of one
score relative to the others rather than the whole
set of data.
WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful Islam
Measures of Location

Quartile

One fourth (1/4)


Decile

One tenth (1/10)


First (1/4), Second (1/2), Third (3/4)
10%, 20%, …90%
Percentile

One of hundreds (1/100)

1%, 2%, ….99%
WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful Islam
Quartile
h
Qi  Li 
fi





i

 n  F , i  1, 2, 3
4

L0 = Lower limit of the i-th Quartile class
n = Total number of observations in the
distribution
h = Class width of the i-th Quartile class
fi = Frequency of the i-th Quartile class
F = Cumulative frequency of the class prior to
the i-th quartile class
WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful Islam
Decile
h
Pi  Li 
fi





 i

 n  F , i  1, 2, 3
 10

L0 = Lower limit of the i-th Decile class
n = Total number of observations in the
distribution
h = Class width of the i-th Decile class
fi = Frequency of the i-th Decile class
F = Cumulative frequency of the class prior to
the i-th Decile class
WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful Islam
Percentile
h
Pi  Li 
fi





 i

n  F , i  1, 2, 3

 100

L0 = Lower limit of the i-th Percentile class
n = Total number of observations in the
distribution
h = Class width of the i-th Percentile class
fi = Frequency of the i-th Percentile class
F = Cumulative frequency of the class prior to
the i-th Percentile class
WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful Islam
Example-1: Percentile of Ungroup
data


Consider the observations 11, 14, 17, 23,
27, 32, 40, 49, 54, 59, 71 and 80. To
determine the 29th percentile?
1
(29 12)  3.48,
100
we note that
which is not an
integer. Thus the next higher integer 4 here
will determine the 29th percentile value.
On inspection P29 = 23
WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful Islam
Example-2: Find 3rd Quartiles, 1st
Decile and 29th Percentile
Marks
No. of students
Cumulative
frequencies
40-50
6
6
50-60
11
17
60-70
19
36
70-80
17
53
80-90
13
66
90-100
4
70
Total
70
WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful Islam
Example-3: Find 30th percentile
Age in years
Number of births
14.5-19.5
19.5-24.5
677
1908
Cumulative number
of births
677
2585
24.5-29.5
29.5-34.5
34.5-39.5
1737
1040
294
4332
5362
5656
39.5-44.5
44.5-49.5
All ages
91
16
5763
5747
5763
-
WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful Islam
Determine Percentile Class
First determine the percentile class.
 If, N =5736, and we have to find 30th
percentile, then percentile class will be the
class which has cumulative frequency
below:

i
n  (30 / 100)  5763 1728.9.
100
WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful Islam
30th Percentile class
1728.9
Age in years
Number of births
14.5-19.5
19.5-24.5
677
1908
Cumulative number
of births
677
2585
24.5-29.5
29.5-34.5
34.5-39.5
1737
1040
294
4332
5362
5656
39.5-44.5
44.5-49.5
All ages
91
16
5763
5747
5763
-