PPT: Standard Deviation & Coefficient of Variance | Engineering Mathematics - Civil Engineering (CE) PDF Download

 Page 1


THE MEAN DEVIATION:-
? The mean deviation of a set of data is defined as 
the arithmetic mean of the deviations measured 
either from the mean or from the median, all 
deviations are being counted as positive.
M.D=                         For sample data
M.D=                         For Population Data
Page 2


THE MEAN DEVIATION:-
? The mean deviation of a set of data is defined as 
the arithmetic mean of the deviations measured 
either from the mean or from the median, all 
deviations are being counted as positive.
M.D=                         For sample data
M.D=                         For Population Data
? Mean Deviation is an absolute measure of 
dispersion. It’s relative measure is known as the co-
efficient of mean deviation, is obtained by dividing 
the mean deviation by the average used in the 
calculation of deviation.
Co-efficient of M.D=               or                 
Example#01: Calculate the  M.D and it’s Co-efficient 
from given data
29,35,38,40,55,60,65,70
Page 3


THE MEAN DEVIATION:-
? The mean deviation of a set of data is defined as 
the arithmetic mean of the deviations measured 
either from the mean or from the median, all 
deviations are being counted as positive.
M.D=                         For sample data
M.D=                         For Population Data
? Mean Deviation is an absolute measure of 
dispersion. It’s relative measure is known as the co-
efficient of mean deviation, is obtained by dividing 
the mean deviation by the average used in the 
calculation of deviation.
Co-efficient of M.D=               or                 
Example#01: Calculate the  M.D and it’s Co-efficient 
from given data
29,35,38,40,55,60,65,70
29              -20                            20
35           -14                      14
38           -11                       11       
40           -9                          9
55            6                          6
60           11                        11
65           16                       16
70           21                        21
?xi=392 ?
=108
Page 4


THE MEAN DEVIATION:-
? The mean deviation of a set of data is defined as 
the arithmetic mean of the deviations measured 
either from the mean or from the median, all 
deviations are being counted as positive.
M.D=                         For sample data
M.D=                         For Population Data
? Mean Deviation is an absolute measure of 
dispersion. It’s relative measure is known as the co-
efficient of mean deviation, is obtained by dividing 
the mean deviation by the average used in the 
calculation of deviation.
Co-efficient of M.D=               or                 
Example#01: Calculate the  M.D and it’s Co-efficient 
from given data
29,35,38,40,55,60,65,70
29              -20                            20
35           -14                      14
38           -11                       11       
40           -9                          9
55            6                          6
60           11                        11
65           16                       16
70           21                        21
?xi=392 ?
=108
putting the values
M.D=
M.D= 13.5 
Now co-efficient of Mean Deviation
Coefficient of M.D=
=
Co-efficient of M.D= 0.27
Page 5


THE MEAN DEVIATION:-
? The mean deviation of a set of data is defined as 
the arithmetic mean of the deviations measured 
either from the mean or from the median, all 
deviations are being counted as positive.
M.D=                         For sample data
M.D=                         For Population Data
? Mean Deviation is an absolute measure of 
dispersion. It’s relative measure is known as the co-
efficient of mean deviation, is obtained by dividing 
the mean deviation by the average used in the 
calculation of deviation.
Co-efficient of M.D=               or                 
Example#01: Calculate the  M.D and it’s Co-efficient 
from given data
29,35,38,40,55,60,65,70
29              -20                            20
35           -14                      14
38           -11                       11       
40           -9                          9
55            6                          6
60           11                        11
65           16                       16
70           21                        21
?xi=392 ?
=108
putting the values
M.D=
M.D= 13.5 
Now co-efficient of Mean Deviation
Coefficient of M.D=
=
Co-efficient of M.D= 0.27
The Variance and Standard Deviation:-
The variance is the set of observations is 
defined as the mean of the deviations of all the 
observation from their mean .When it is calculated from
the entire population, the variance is called population 
variance. If instead, the data from sample  are used to 
calculate the variance, it is referred to as the sample 
variance. The symbolic definition for variance is 
=                   , For population data
, For sample data
=