Revision Notes: Statistics

# 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
?
?
? ?
?
?
```

## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

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