Statistics: Class 10 Mathematics NCERT Chapter 14

Key Features of NCERT Material for Class 10 Mathematics Chapter 14 – Statistics

In the last chapter 13, you learned about surface areas and volumes. In this chapter, you will learn about Statistics.

Ungrouped Data 

Ungrouped data will be data in its unique or crude structure. The observations are not classified into gatherings. 

For instance, the ages of everybody present in a classroom of kindergarten kids with the educator is as per the following: 

3, 3, 4, 3, 5, 4, 3, 3, 4, 3, 3, 3, 3, 4, 3, 27. 


This data shows that there is one grown-up present in this class and that is the educator. Ungrouped data is anything but difficult to work when the data set is little. 

Grouped Data 

In grouped data, observations are sorted out in gatherings. 

For instance, a class of students got various grades in a school test. The data is arranged as follows: 

This shows what number of students got the specific grades. Grouped data is simpler to work with when a lot of data is available. 


Frequency is the occasion when a specific observation happens in data. 

Class Interval 

Data can be grouped into class intervals with the end goal that all observations in that range have a place with that class. 

Class width is equal to upper class limit– lower class limit 

Cumulative Frequency 

Cumulative frequency is gotten by adding all the frequencies in a specific way. 

Cumulative Frequency distribution of lesser than type 

Cumulative frequency of lesser than type demonstrates the quantity of observations which are not exactly or equivalent to a specific observation. 

Cumulative Frequency distribution of more than type 

Cumulative frequency of more than type demonstrates the quantity of observations which are more prominent than or equivalent to a specific observation. 

MEAN (AVERAGE): Mean [Ungrouped Data] – Mean of n observations, x1, x2, x3 … xn, is 


MEAN [Grouped Data]: The mean for grouped data can be found by the accompanying three strategies: 

(I) Direct Mean Method: 


Class Mark =  4-23

Note: Frequency of a class is focused at its mid-point called class mark. 

(ii) Assumed Mean Method: In this, a subjective mean ‘a’ is picked which is called, ‘accepted mean’, some place in all the estimations of x. 


… [where di = (xi – a)] 

(iii) Step Deviation Method: 

… .. [where , where h is a typical divisor of di] 

MEDIAN: Median is a proportion of central propensity which gives the estimation of the center most observation in the data. 


… where[l = Lower breaking point of median class; n = Number of observations; f = Frequency of median class; c.f. = Cumulative frequency of going before class; h = Class size] 

(iii) Showing a cumulative frequency distribution graphically as a cumulative frequency curve, or an ogive of the lesser than type and of the more than type. The median of grouped data can be gotten graphically as the x-coordinate of the point of intersection of the two ogives for this data. 

Significant relations between strategies for discovering mean 

  • Every one of the three techniques for discovering mean yield a similar outcome. 
  • Step deviation strategy is simpler to apply if all the deviations have a typical factor. 
  • Assumed mean technique and step deviation strategy are simplified adaptations of the direct technique. 


(I) Ungrouped Data: The estimation of the observation having the most extreme frequency is the mode. 

(ii) Grouped Data


… where[l = Lower breaking point of modal class; f1 = Frequency of modal class; f0 = Frequency of the class going before the modal class; f2 = Frequency of the class after the modal class; h = Size of class interval. c.f. = Cumulative frequency of going before class; h = Class size] 

Mode = 3 Median – 2 Mean 

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