# 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 MEAN [Grouped Data]: The mean for grouped data can be found by the following three methods:
(i) Direct Mean Method: 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. …[where di = (xi – a)]

(iii) Step Deviation Method: ….. [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.

### …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: …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

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