NCERT CBSE Class 10th Mathematics Chapter 14: Statistics

Safalta Expert Published by: Sylvester Updated Wed, 22 Jun 2022 06:54 PM IST

Highlights

NCERT CBSE Class 10th Mathematics Chapter 14: Statistics

The fourteenth chapter in Mathematics textbook is 'Statistics'.


Mean

MEAN (AVERAGE): Mean [Ungrouped Data] – Mean of n observations, x1, x2, x3 … xn, is
Statistics Class 10 Notes Maths Chapter 14 1

MEAN [Grouped Data]: The mean for grouped data can be found by the following three methods:
(i) Direct Mean Method:
Statistics Class 10 Notes Maths Chapter 14 2
Class Mark = UpperClassLimit+LowerClassLimit upon 2
 

(ii) Assumed Mean Method: In this, an arbitrary mean ‘a’ is chosen which is called, ‘assumed mean’, somewhere in the middle of all the values of x.
Statistics Class 10 Notes Maths Chapter 14 3
…[where di = (xi – a)]

(iii) Step Deviation Method:
Statistics Class 10 Notes Maths Chapter 14 4
….. [where ui=dih , where h is a common divisor of di]

 

Median

Median is a measure of central tendency which gives the value of the middle-most observation in the data.

Statistics Class 10 Notes Maths Chapter 14 5

…where[l = Lower limit of median class; n = Number of observations; f = Frequency of median class; c.f. = Cumulative frequency of preceding class; h = Class size]



Mode

(i) Ungrouped Data: The value of the observation having maximum frequency is the mode.
(ii) Grouped Data:
Statistics Class 10 Notes Maths Chapter 14 6
…where[l = Lower limit of modal class; f1 = Frequency of modal class; f0 = Frequency of the class preceding the modal class; f2 = Frequency of the class succeeding the modal class; h = Size of class interval. c.f. = Cumulative frequency of preceding class; h = Class size]

Mode = 3 Median – 2 Mean
Median = Mode+2Mean upon 3
Mean = 3Median−Mode upon 2


The topics discussed in this chapter are as follows:

  • Ungrouped Data
  • Grouped Data
  • Frequency and Class Interval
  • Mean, Median and Mode
  • Ogive

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Cumulative frequency curve is also called

ogive

The relationship between mean, median and mode for a moderately skewed distribution is

mode = 3 median – 2 mean

Mode and mean of a data are 12k and 15A. Median of the data is

Mode = 3 median – 2 mean
⇒ 12k = 3 median – 2 × 15k
⇒ 42k = 3 median
⇒ Median = 14k

While computing mean of grouped data, we assume that the frequencies are

centred at the classmarks of the classes

Mode is the

maximum frequent value

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