The following distribution gives the daily income of 50 workers of a factory. Daily income 100 - 120 120 - 140 140 - 160 160 - 180 180 - 200 Number of workers 12 14 8 6 10 Convert the above distribution to a less than type cumulative frequency distribution, and draw its ogive.

We can convert the given distribution table into frequency distribution table of less than type as follows : Daily income (in ₹) (upper class limits) Cumulative frequency Less than 120 12 Less than 140 12 + 14 = 26 Less than 160 26 + 8 = 34 Less than 180 34 + 6 = 40 Less than 200 40 + 10 = 50 Now, on x - axis we take upper class limits of class intervals and their respective cumulative frequencies on y - axis. We can draw its ogive as follows :

During the medical check-up of 35 students of a class, their weights were recorded as follows: Weight (in kg ) Number of students Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 35 Draw a less than type ogive for the given data. Hence, obtain the median weight from the graph verify the result by using the formula.

The cumulative frequency distributions of less than type is given as Weight (in kg ) upper class limits Number of students (cumulative frequency) Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 35 Now, on x - axis we take upper class limits of class intervals and their respective cumulative frequencies on y - axis we can draw its ogive as follows : Now mark the point A whose ordinate is 17 . 5 its abscissa is 46 . 5 . So median of this data is 46 . 5 . We can see from the table that difference between two consecutive upper-class limits is 2 . Now we have to obtain class marks with their respective frequencies as below : Weight (in kg) Frequency (f) Cumulative frequency Less than 38 0 0 38 - 40 3 - 0 = 3 3 40 - 42 5 - 3 = 2 5 42 - 44 9 - 5 = 4 9 44 - 46 14 - 9 = 5 14 46 - 48 28 - 14 = 14 28 48 - 50 32 - 28 = 4 32 50 - 52 35 - 32 = 3 35 Total ( n ) 35 Here, n = 35 . So, n 2 = 17.5 Now the cumulative frequency just greater than n 2 i . e . , 35 2 = 17.5 is 28 . It belongs to class interval 46 – 48 So, Median class = 46 – 48 Lower class limit ( l ) of median class = 46 Frequency ( f ) of median class = 14 Cumulative frequency ( c f ) of class preceding median class = 14 Class size ( h ) = 2 M e d i a n = l + n 2 - c f f × h = 46 + 17.5 - 14 14 × 2 = 46 + 3.5 7 = 46 + 0.5 = 46 . 5 So, median of this data is 46 . 5 . Hence, value of median is verified.

The following table gives production yield per hectare of wheat of 100 farms of a village. Production yield (in kg / ha ) 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80 Number of farms 2 8 12 24 38 16 Change the distribution to a more than type distribution and draw ogive.

We can obtain cumulative frequency distribution of more than type as following Production yield Cumulative frequency more than or equal to 50 100 more than or equal to 55 100 - 2 = 98 more than or equal to 60 98 - 8 = 90 more than or equal to 65 90 - 12 = 78 more than or equal to 70 78 - 24 = 54 more than or equal to 75 54 - 38 = 16 Now, on x - axis we take upper class limits of class intervals and their respective cumulative frequencies on y - axis we can draw its ogive as following.

E M B I B E

MATHEMATICS - Class X>Chapter 14 - Statistics>Exercise 14.4

Exercise 14.4

Author:Jharkhand Board

Jharkhand Board Mathematics Solutions for Exercise 14.4

Simple step-by-step solutions to Exercise 14.4 questions of Statistics from MATHEMATICS - Class X. Also get 3D topic explainers, cheat sheets, and unlimited doubts solving on EMBIBE.

Questions from Exercise 14.4 with Hints & Solutions

EASY

10th Jharkhand Board

IMPORTANT

MATHEMATICS - Class X>Chapter 14 - Statistics>Exercise 14.4>Q 1

The following distribution gives the daily income of $50$ workers of a factory.

Daily income	$100 - 120$	$120 - 140$	$140 - 160$	$160 - 180$	$180 - 200$
Number of workers	$12$	$14$	$8$	$6$	$10$

Convert the above distribution to a less than type cumulative frequency distribution, and draw its ogive.

MEDIUM

10th Jharkhand Board

IMPORTANT

MATHEMATICS - Class X>Chapter 14 - Statistics>Exercise 14.4>Q 2

During the medical check-up of $35$ students of a class, their weights were recorded as follows:

Weight (in $kg$ )	Number of students
Less than $38$	$0$
Less than $40$	$3$
Less than $42$	$5$
Less than $44$	$9$
Less than $46$	$14$
Less than $48$	$28$
Less than $50$	$32$
Less than $52$	$35$