02 - Let's Recap - Statistics - Class 10 -Maths Class 10 Notes | EduRev

Crash Course for Class 10 Maths by Let's tute

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Class 10 : 02 - Let's Recap - Statistics - Class 10 -Maths Class 10 Notes | EduRev

 Page 1


 
(Statistics is the branch of Mathematics dealing with the collection, organization, 
and interpretation of numerical data) 
 
1. In statistics, a central tendency (or, more commonly, a measure of central tendency) is 
a central value or a typical value for a probability distribution. It is occasionally called 
an average or just the center of the distribution. The most common measures of central 
tendency are 
a. The arithmetic mean or mean 
b.  The median and 
c.  The mode. 
 
2.            (  )             
                                     
 
 
 
3. Mean of grouped data:  
The mean (or average) of observations is the sum of the values of all the 
observations divided by the total number of observations. 
It can be found by three methods:  
 
I. THE DIRECT METHOD 
 
x
  
 
 
 
 
  
 
 
 
       
 
 
 
 
 
  
 
    
 
     
? 
 
 
 
? 
 
 
 
Where, 
x
   mean, 
? = Sum operation, 
 
 
 = frequency of the observations of a data, 
 
 
 = Midvalue of the observations of a data, 
 
 
 
 
 = Product of midvalue of the observations and their corresponding frequencies of a 
data, 
  = varies from 1 to n 
 
 
Page 2


 
(Statistics is the branch of Mathematics dealing with the collection, organization, 
and interpretation of numerical data) 
 
1. In statistics, a central tendency (or, more commonly, a measure of central tendency) is 
a central value or a typical value for a probability distribution. It is occasionally called 
an average or just the center of the distribution. The most common measures of central 
tendency are 
a. The arithmetic mean or mean 
b.  The median and 
c.  The mode. 
 
2.            (  )             
                                     
 
 
 
3. Mean of grouped data:  
The mean (or average) of observations is the sum of the values of all the 
observations divided by the total number of observations. 
It can be found by three methods:  
 
I. THE DIRECT METHOD 
 
x
  
 
 
 
 
  
 
 
 
       
 
 
 
 
 
  
 
    
 
     
? 
 
 
 
? 
 
 
 
Where, 
x
   mean, 
? = Sum operation, 
 
 
 = frequency of the observations of a data, 
 
 
 = Midvalue of the observations of a data, 
 
 
 
 
 = Product of midvalue of the observations and their corresponding frequencies of a 
data, 
  = varies from 1 to n 
 
 
 
 
II. THE ASSUMED MEAN METHOD 
 
x
    
? 
 
 
 
? 
 
 
Where, 
x
   mean, 
? = Sum operation, 
 
 
 = frequency of the observations of a data, 
 
 
 = deviations = (midvalues   assumed mean) 
                           ( 
 
  ) , 
 
 
 
 
 = Product of midvalue of the observations and their corresponding frequencies 
  
  = varies from 1 to n 
 
III. THE STEP DEVIATION METHOD 
 
x
    (
? 
 
 
 
? 
 
)   
Where, 
 
x
   mean, 
? = sum operation, 
 = assumed mean, 
 
 
 = frequency of the observations of a data, 
  = class size, 
 
 
 = ratio of deviations and a common number  
 
 
  
 
 
 
 
 
, 
  = varies from 1 to n 
Page 3


 
(Statistics is the branch of Mathematics dealing with the collection, organization, 
and interpretation of numerical data) 
 
1. In statistics, a central tendency (or, more commonly, a measure of central tendency) is 
a central value or a typical value for a probability distribution. It is occasionally called 
an average or just the center of the distribution. The most common measures of central 
tendency are 
a. The arithmetic mean or mean 
b.  The median and 
c.  The mode. 
 
2.            (  )             
                                     
 
 
 
3. Mean of grouped data:  
The mean (or average) of observations is the sum of the values of all the 
observations divided by the total number of observations. 
It can be found by three methods:  
 
I. THE DIRECT METHOD 
 
x
  
 
 
 
 
  
 
 
 
       
 
 
 
 
 
  
 
    
 
     
? 
 
 
 
? 
 
 
 
Where, 
x
   mean, 
? = Sum operation, 
 
 
 = frequency of the observations of a data, 
 
 
 = Midvalue of the observations of a data, 
 
 
 
 
 = Product of midvalue of the observations and their corresponding frequencies of a 
data, 
  = varies from 1 to n 
 
 
 
 
II. THE ASSUMED MEAN METHOD 
 
x
    
? 
 
 
 
? 
 
 
Where, 
x
   mean, 
? = Sum operation, 
 
 
 = frequency of the observations of a data, 
 
 
 = deviations = (midvalues   assumed mean) 
                           ( 
 
  ) , 
 
 
 
 
 = Product of midvalue of the observations and their corresponding frequencies 
  
  = varies from 1 to n 
 
III. THE STEP DEVIATION METHOD 
 
x
    (
? 
 
 
 
? 
 
)   
Where, 
 
x
   mean, 
? = sum operation, 
 = assumed mean, 
 
 
 = frequency of the observations of a data, 
  = class size, 
 
 
 = ratio of deviations and a common number  
 
 
  
 
 
 
 
 
, 
  = varies from 1 to n 
 
 
4. Mode of grouped data:  
A mode is that value among the observations which occurs most often, that is, the 
value of the observation having the maximum frequency. 
A class with the maximum frequency, called the modal class and the mode is a 
value inside the modal class. 
 
  (
 
 
  
 
  
 
  
 
  
 
)   
 
Where, 
 = lower limit of the modal class, 
 
 
= frequency of the modal class, 
 
 
= frequency of the class, preceding the modal class, 
 
 
= frequency of the class succeeding the modal class, 
 = class size (assuming all class sizes to be equal) 
 
 
5. The cumulative frequency of a class is the frequency obtained by adding the frequencies 
of all the classes preceding the given class. 
 
 
6. Median of grouped data:  
A median is a value that is positioned exactly in the middle of the set of 
observations arranged in an ascending or descending order. Hence, it separates the higher 
half of a data from the lower half. 
A class whose cumulative frequency is greater than (and nearest to) 
 
 
, i.e., half of 
the total frequency of a data, is called the median class and the median is a value inside 
the median class. 
 
  (
 
 
   
 
)   
 
Page 4


 
(Statistics is the branch of Mathematics dealing with the collection, organization, 
and interpretation of numerical data) 
 
1. In statistics, a central tendency (or, more commonly, a measure of central tendency) is 
a central value or a typical value for a probability distribution. It is occasionally called 
an average or just the center of the distribution. The most common measures of central 
tendency are 
a. The arithmetic mean or mean 
b.  The median and 
c.  The mode. 
 
2.            (  )             
                                     
 
 
 
3. Mean of grouped data:  
The mean (or average) of observations is the sum of the values of all the 
observations divided by the total number of observations. 
It can be found by three methods:  
 
I. THE DIRECT METHOD 
 
x
  
 
 
 
 
  
 
 
 
       
 
 
 
 
 
  
 
    
 
     
? 
 
 
 
? 
 
 
 
Where, 
x
   mean, 
? = Sum operation, 
 
 
 = frequency of the observations of a data, 
 
 
 = Midvalue of the observations of a data, 
 
 
 
 
 = Product of midvalue of the observations and their corresponding frequencies of a 
data, 
  = varies from 1 to n 
 
 
 
 
II. THE ASSUMED MEAN METHOD 
 
x
    
? 
 
 
 
? 
 
 
Where, 
x
   mean, 
? = Sum operation, 
 
 
 = frequency of the observations of a data, 
 
 
 = deviations = (midvalues   assumed mean) 
                           ( 
 
  ) , 
 
 
 
 
 = Product of midvalue of the observations and their corresponding frequencies 
  
  = varies from 1 to n 
 
III. THE STEP DEVIATION METHOD 
 
x
    (
? 
 
 
 
? 
 
)   
Where, 
 
x
   mean, 
? = sum operation, 
 = assumed mean, 
 
 
 = frequency of the observations of a data, 
  = class size, 
 
 
 = ratio of deviations and a common number  
 
 
  
 
 
 
 
 
, 
  = varies from 1 to n 
 
 
4. Mode of grouped data:  
A mode is that value among the observations which occurs most often, that is, the 
value of the observation having the maximum frequency. 
A class with the maximum frequency, called the modal class and the mode is a 
value inside the modal class. 
 
  (
 
 
  
 
  
 
  
 
  
 
)   
 
Where, 
 = lower limit of the modal class, 
 
 
= frequency of the modal class, 
 
 
= frequency of the class, preceding the modal class, 
 
 
= frequency of the class succeeding the modal class, 
 = class size (assuming all class sizes to be equal) 
 
 
5. The cumulative frequency of a class is the frequency obtained by adding the frequencies 
of all the classes preceding the given class. 
 
 
6. Median of grouped data:  
A median is a value that is positioned exactly in the middle of the set of 
observations arranged in an ascending or descending order. Hence, it separates the higher 
half of a data from the lower half. 
A class whose cumulative frequency is greater than (and nearest to) 
 
 
, i.e., half of 
the total frequency of a data, is called the median class and the median is a value inside 
the median class. 
 
  (
 
 
   
 
)   
 
 
 
 
 
Where, 
 = lower limit of the modal class, 
  ?  
 
= Total frequency, 
  =Cumulative frequency of class preceding the median class, 
f =
 
Frequency of the median class, 
 = class size (assuming all class sizes to be equal) 
 
7. Cumulative frequency distribution can be represented graphically as a cumulative 
frequency curve (an ogive) of a less than type and of the more than type. 
 
 
8. The median of a grouped data can be obtained graphically as the  -coordinate of the 
point of intersection of the two ogives (‘Less than’ & ‘More than’) for a data. 
 
 
 
 
 
 
 
 
 
 
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