Statistics Class 11 Notes Maths Chapter 13

 Page 1


 
KEY POINTS
? Range of Ungrouped Data and Discrete Frequency  
Distribution = Largest observation – smallest observation. 
? Range of Continuous FrequencyDistribution 
= Upper Limit of Highest Class — Lower Limit of Lowest Class 
? Mean deviation for ungrouped data or raw data 
? ?
| |
. .
i
x x
M D x
n
?
?
?
? ?
| |
. . ,
i
x M
M D M where M Median
n
?
? ?
?
 
? Mean deviation for grouped data (Discrete frequency distribution 
and Continuous frequency distribution). 
? ?
| |
. .
i i
f x x
M D x
N
?
?
?
,where N = ? fi 
Page 2


 
KEY POINTS
? Range of Ungrouped Data and Discrete Frequency  
Distribution = Largest observation – smallest observation. 
? Range of Continuous FrequencyDistribution 
= Upper Limit of Highest Class — Lower Limit of Lowest Class 
? Mean deviation for ungrouped data or raw data 
? ?
| |
. .
i
x x
M D x
n
?
?
?
? ?
| |
. . ,
i
x M
M D M where M Median
n
?
? ?
?
 
? Mean deviation for grouped data (Discrete frequency distribution 
and Continuous frequency distribution). 
? ?
| |
. .
i i
f x x
M D x
N
?
?
?
,where N = ? fi 
 
? ?
| |
. .
i i
f x M
M D M
N
?
?
?
, where N = ? fi 
? Variance is defined as the mean of the squares of the deviations 
from mean. 
? Standard deviation ‘ ? ’ is positive square root of variance.
va ria n ce ? ? 
? variance ?
2
 and standard deviation (SD) ? for ungrouped data
? ?
2
2
1
i
x x
n
? ? ? ?
? ?
2
1
i
SD x x
n
? ? ? ? ?
? Standard deviation of a discrete frequency distribution 
? ? ? ?
2
2
2
1 1
i i i i i
f x x N f x f x
N N
? ? ? ? ?
? ? ?
? Standard deviation of a continuous frequency distribution 
? ? ? ?
2
2
2
1 1
i i i i i
f x x N f x f x
N N
? ? ? ? ?
? ? ?
where xi are the midpoints of the classes. 
? Short cut method to find variance and standard deviation 
? ?
2
2
2
2 i i i i
h
N f y f y
N
?
? ?
? ?
? ?
? ?
? ?
? ?
2
2
i i i i
h
N f y f y
N
? ? ?
? ?
Page 3


 
KEY POINTS
? Range of Ungrouped Data and Discrete Frequency  
Distribution = Largest observation – smallest observation. 
? Range of Continuous FrequencyDistribution 
= Upper Limit of Highest Class — Lower Limit of Lowest Class 
? Mean deviation for ungrouped data or raw data 
? ?
| |
. .
i
x x
M D x
n
?
?
?
? ?
| |
. . ,
i
x M
M D M where M Median
n
?
? ?
?
 
? Mean deviation for grouped data (Discrete frequency distribution 
and Continuous frequency distribution). 
? ?
| |
. .
i i
f x x
M D x
N
?
?
?
,where N = ? fi 
 
? ?
| |
. .
i i
f x M
M D M
N
?
?
?
, where N = ? fi 
? Variance is defined as the mean of the squares of the deviations 
from mean. 
? Standard deviation ‘ ? ’ is positive square root of variance.
va ria n ce ? ? 
? variance ?
2
 and standard deviation (SD) ? for ungrouped data
? ?
2
2
1
i
x x
n
? ? ? ?
? ?
2
1
i
SD x x
n
? ? ? ? ?
? Standard deviation of a discrete frequency distribution 
? ? ? ?
2
2
2
1 1
i i i i i
f x x N f x f x
N N
? ? ? ? ?
? ? ?
? Standard deviation of a continuous frequency distribution 
? ? ? ?
2
2
2
1 1
i i i i i
f x x N f x f x
N N
? ? ? ? ?
? ? ?
where xi are the midpoints of the classes. 
? Short cut method to find variance and standard deviation 
? ?
2
2
2
2 i i i i
h
N f y f y
N
?
? ?
? ?
? ?
? ?
? ?
? ?
2
2
i i i i
h
N f y f y
N
? ? ?
? ?
 
Where 
i
i
x A
y
h
?
?
? Coefficient of variation ?C.V ? ?
100, 0 x
x
?
? ? ?
? If each observation is multiplied by a positive constant k then 
variance of the resulting observations become k
2
 times of the 
original value and standard deviation becomes k times of the 
original value. 
? If each observation is increased by k, where k is positive or 
negative, the variance and standard deviation remains same. 
? Standard deviation is independent of choice of origin but 
depends on the scale of measurement. 
? The series having higher coefficient of variation is called more 
variable than the other. While the series having lesser coefficient 
of variation is called more consistent or more stable. For series 
with equal means the series with lesser standard deviation is 
more stable. 
? The mean and standard deviation of a set of 
1
n observations 
are 
1
x and 
1
s respectively while the mean and standard 
deviation of another set of 
2
n observations are 
2
x and 
2
s 
respectively then the standard deviation of the combined set of 
? ?
1 2
n n ? observations is given by 
? ? ? ?
? ?
? ?
2
2 2
1 2 1 2
1 1 2 2
2
1 2
1 2
.
n n x x
n s n s
S D
n n
n n
?
?
? ?
?
?