NCERT Solutions Class 10 Maths Chapter 13 Statistics on Padhaiwise

NCERT Solutions for Class 10 Maths Chapter 13 Statistics Exercise 13.1

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 10 Maths Chapter 13 Statistics Exercise 13.1#

Exercise 13.1 covers three methods of finding the mean of grouped data: Direct Method, Assumed Mean Method, and Step Deviation Method.

Methods to Find Mean of Grouped Data:

Direct Method: $\bar{x} = \dfrac{\sum f_i x_i}{\sum f_i}$
Assumed Mean Method: $\bar{x} = a + \dfrac{\sum f_i d_i}{\sum f_i}$, where $d_i = x_i - a$
Step Deviation Method: $\bar{x} = a + \dfrac{\sum f_i u_i}{\sum f_i} \times h$, where $u_i = \dfrac{x_i - a}{h}$

1. A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house. #

Answer

Number of plants	Number of houses ($f_i$)	$x_i$	$f_i x_i$
0-2	1	1	1
2-4	2	3	6
4-6	1	5	5
6-8	5	7	35
8-10	6	9	54
10-12	2	11	22
12-14	3	13	39
Total	20		162

Using $\bar{x} = \dfrac{\sum f_i x_i}{\sum f_i}$:

NCERT Solutions for Class 10 Maths Chapter 13 Statistics Exercise 13.2

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 10 Maths Chapter 13 Statistics Exercise 13.2#

Exercise 13.2 covers finding the mode of grouped data using the mode formula.

Mode of Grouped Data:
$$\text{Mode} = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h$$
where $l$ = lower class limit of modal class, $f_1$ = frequency of modal class, $f_0$ = frequency of class preceding modal class, $f_2$ = frequency of class succeeding modal class, $h$ = class size.

NCERT Solutions for Class 10 Maths Chapter 13 Statistics Exercise 13.3

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 10 Maths Chapter 13 Statistics Exercise 13.3#

Exercise 13.3 covers finding the median of grouped data using the median formula.

Median of Grouped Data:
$$\text{Median} = l + \frac{\frac{n}{2} - cf}{f} \times h$$
where $l$ = lower class limit of median class, $n$ = total frequency, $cf$ = cumulative frequency of class preceding median class, $f$ = frequency of median class, $h$ = class size. The median class is the class where cumulative frequency first exceeds $\dfrac{n}{2}$.