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# Points to Remember: Statistics Class 10 Notes | EduRev

## Class 10 : Points to Remember: Statistics Class 10 Notes | EduRev

``` Page 1

Statistics
Page 2

Statistics
When a form of solid is converted into another one,
surface area may change but volume remains the same.
Hence, we equate the formula of volume of the other object,
to the value (in numbers) of the volume of the original object
to know the value of the new parameter.
Calculate product of each “u? ” with
corresponding frequency “ƒ?  ” name it as “ u?    ƒ?  ”
Arrange the data in increasing order
Upper Limit         Lower Limit
Assume a mean ‘a’ of the given data values x? ’s :
If the class intervals are odd in number then mid value of centermost class interval will be assumed as Mean.
If the class intervals are even in number then the mid value of class interval having greater frequency will be
assumed mean. Calculate the deviation of each mid value from assumed mean ‘a’ as d?  = x?  - a
Calculate product of each “d? ” with
corresponding frequency “ƒ?  ” name it as “d?    ƒ?  ”
Calculate sum of all  ƒ?   ’ s and “d?    ƒ?   ’s ”
Calculate sum of all  ƒ?  ‘s and “ u?    ƒ?   ’s ”
Mean of Grouped Data
DIRECT METHOD ASSUMED MEAN METHOD STEP DEVIATION METHOD
Calculate the product of each “x? ” with
corresponding frequency “ƒ?  ” name it as“ x?    ƒ?  ”
Calculate sum of all ƒ?   ’ s and “x?    ƒ?   ’s ”
Calculate the range of data and then divide into class intervals of same class size. Calculate x? (Mid value) = (UL + LL)
1
2
Use to nd mean. x = a +
? d?    ƒ?
?  ƒ?
Use to nd mean. x = a +
? u?    ƒ?
? ƒ?
( (
x h
Now, divide it by the class interval size ‘h’ , denote
it as
u?  =
x?  - a
h
Use
to nd mean. x =
? x?  ƒ ?
? ƒ ?
Mean of Ungrouped Data
1 2 3
x
=
n

?
x
i

h
-  Class interval (size)
x
i
-  Observations
n -  Number of Observations
x

-  Mean
f
i
-  Frequency
STATISTICS 32
Statistics
Page 3

Statistics
When a form of solid is converted into another one,
surface area may change but volume remains the same.
Hence, we equate the formula of volume of the other object,
to the value (in numbers) of the volume of the original object
to know the value of the new parameter.
Calculate product of each “u? ” with
corresponding frequency “ƒ?  ” name it as “ u?    ƒ?  ”
Arrange the data in increasing order
Upper Limit         Lower Limit
Assume a mean ‘a’ of the given data values x? ’s :
If the class intervals are odd in number then mid value of centermost class interval will be assumed as Mean.
If the class intervals are even in number then the mid value of class interval having greater frequency will be
assumed mean. Calculate the deviation of each mid value from assumed mean ‘a’ as d?  = x?  - a
Calculate product of each “d? ” with
corresponding frequency “ƒ?  ” name it as “d?    ƒ?  ”
Calculate sum of all  ƒ?   ’ s and “d?    ƒ?   ’s ”
Calculate sum of all  ƒ?  ‘s and “ u?    ƒ?   ’s ”
Mean of Grouped Data
DIRECT METHOD ASSUMED MEAN METHOD STEP DEVIATION METHOD
Calculate the product of each “x? ” with
corresponding frequency “ƒ?  ” name it as“ x?    ƒ?  ”
Calculate sum of all ƒ?   ’ s and “x?    ƒ?   ’s ”
Calculate the range of data and then divide into class intervals of same class size. Calculate x? (Mid value) = (UL + LL)
1
2
Use to nd mean. x = a +
? d?    ƒ?
?  ƒ?
Use to nd mean. x = a +
? u?    ƒ?
? ƒ?
( (
x h
Now, divide it by the class interval size ‘h’ , denote
it as
u?  =
x?  - a
h
Use
to nd mean. x =
? x?  ƒ ?
? ƒ ?
Mean of Ungrouped Data
1 2 3
x
=
n

?
x
i

h
-  Class interval (size)
x
i
-  Observations
n -  Number of Observations
x

-  Mean
f
i
-  Frequency
STATISTICS 32
Statistics
Mode of Grouped Data Median of Grouped Data
Mode of Ungrouped Data Median of Ungrouped Data
Observe the greatest frequency ( f
1
) and so the corresponding class
will be modal class.
Pen down ‘l’ = lower limit of modal class
Pen down ‘l’ = lower limit of median class
Note down the frequency of class preceding the modal class ( f
0
) &
the frequency of class succeeding the modal class ( f
2
).
Note down the cumulative frequency of class preceding the median
class (c.f.) & the frequency of median class ( f ).
Calculate class size ‘h’ as h = ( UL - LL )
Calculate class size ‘h’ as h = ( UL - LL )
Mode  = l
+
x  h
ƒ
1

-
ƒ
0

2 ƒ
1

-
ƒ
0

-
ƒ
2
( (
Use this to nd mode.
Observe that and Calculate
n
=  ?  ƒ ?
n
2
Calculate the cumulative frequencies (c. f.) of all the classes.
Observe the cumulative frequency just greater than          and
determine the corresponding class as median class.
n
2
Use this to nd median. Median  = l
+
-
c
ƒ

ƒ
( (
n
2
x  h
It is the most frequent value of the obsevation i.e. the observation
possessing maximum frequency.
When n is even mean of the two centermost values median =
{ {
When n is odd median =
n
2
STATISTICS 33
Page 4

Statistics
When a form of solid is converted into another one,
surface area may change but volume remains the same.
Hence, we equate the formula of volume of the other object,
to the value (in numbers) of the volume of the original object
to know the value of the new parameter.
Calculate product of each “u? ” with
corresponding frequency “ƒ?  ” name it as “ u?    ƒ?  ”
Arrange the data in increasing order
Upper Limit         Lower Limit
Assume a mean ‘a’ of the given data values x? ’s :
If the class intervals are odd in number then mid value of centermost class interval will be assumed as Mean.
If the class intervals are even in number then the mid value of class interval having greater frequency will be
assumed mean. Calculate the deviation of each mid value from assumed mean ‘a’ as d?  = x?  - a
Calculate product of each “d? ” with
corresponding frequency “ƒ?  ” name it as “d?    ƒ?  ”
Calculate sum of all  ƒ?   ’ s and “d?    ƒ?   ’s ”
Calculate sum of all  ƒ?  ‘s and “ u?    ƒ?   ’s ”
Mean of Grouped Data
DIRECT METHOD ASSUMED MEAN METHOD STEP DEVIATION METHOD
Calculate the product of each “x? ” with
corresponding frequency “ƒ?  ” name it as“ x?    ƒ?  ”
Calculate sum of all ƒ?   ’ s and “x?    ƒ?   ’s ”
Calculate the range of data and then divide into class intervals of same class size. Calculate x? (Mid value) = (UL + LL)
1
2
Use to nd mean. x = a +
? d?    ƒ?
?  ƒ?
Use to nd mean. x = a +
? u?    ƒ?
? ƒ?
( (
x h
Now, divide it by the class interval size ‘h’ , denote
it as
u?  =
x?  - a
h
Use
to nd mean. x =
? x?  ƒ ?
? ƒ ?
Mean of Ungrouped Data
1 2 3
x
=
n

?
x
i

h
-  Class interval (size)
x
i
-  Observations
n -  Number of Observations
x

-  Mean
f
i
-  Frequency
STATISTICS 32
Statistics
Mode of Grouped Data Median of Grouped Data
Mode of Ungrouped Data Median of Ungrouped Data
Observe the greatest frequency ( f
1
) and so the corresponding class
will be modal class.
Pen down ‘l’ = lower limit of modal class
Pen down ‘l’ = lower limit of median class
Note down the frequency of class preceding the modal class ( f
0
) &
the frequency of class succeeding the modal class ( f
2
).
Note down the cumulative frequency of class preceding the median
class (c.f.) & the frequency of median class ( f ).
Calculate class size ‘h’ as h = ( UL - LL )
Calculate class size ‘h’ as h = ( UL - LL )
Mode  = l
+
x  h
ƒ
1

-
ƒ
0

2 ƒ
1

-
ƒ
0

-
ƒ
2
( (
Use this to nd mode.
Observe that and Calculate
n
=  ?  ƒ ?
n
2
Calculate the cumulative frequencies (c. f.) of all the classes.
Observe the cumulative frequency just greater than          and
determine the corresponding class as median class.
n
2
Use this to nd median. Median  = l
+
-
c
ƒ

ƒ
( (
n
2
x  h
It is the most frequent value of the obsevation i.e. the observation
possessing maximum frequency.
When n is even mean of the two centermost values median =
{ {
When n is odd median =
n
2
STATISTICS 33
Median of
Grouped Data
Introduction to
Statistics

Mean of
Grouped Data

Cumulative frequency -
Less Than Type

Cumulative Frequency -
More Than Type
Scan the QR Codes to watch our free videos
For nding median in an ungrouped data, please write the data
in ascending or descending order rst.
Mean – Mode = 3 (Mean - Median) approximately.
An ungrouped data may not have a mode when there is no
observation that occurs with highest frequency.
PLEASE KEEP IN MIND
UNGROUPED DATA
GROUPED DATA
?
?
If all the values are increased by a certain percentage/amount
then mean also gets increased by the same percentage/amount.
?
A set of grouped data modal class is the class with largest
frequency.
?
In a grouped data, the value of mean, median or mode will
never exceed the respective class intervals.
?
In the case of grouped data, make the class intervals
continuous if they are not. This can be done by reducing the lower
limit by 0.5 and increasing the upper limit by 0.5.
?
?
STATISTICS 34
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