During the medical check-up of 35 students of a class, their weights were recorded as follows: Weight (in kg)Number of studentsLess than 38Less than 40Less than 42Less than 44Less than 46Less than 48Less than 50Less than 52035914283235Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.

Question

Filo · Accepted Answer

Let us now plot the points corresponding to the ordered pairs given by

(38, 0), (40, 3), (42, 5), (44, 9), (46, 14), (48, 28), (50, 32)

and

(52, 35)

on a graph paper and join them by a free hand smooth curve.

Now,

Weight (in kg)	Number of students (Frequency)
$0 - 38$	$0$
$38 - 40$	$3 - 0 = 3$
$40 - 42$	$5 - 3 = 2$
$42 - 44$	$9 - 5 = 4$
$44 - 46$	$14 - 9 = 5$
$46 - 48$	$28 - 14 = 14$
$48 - 50$	$32 - 28 = 4$
$50 - 52$	$35 - 32 = 3$

Mode: The class which have highest frequency.

In this case, class interval

46 - 48

is the modal class.

Now,

Lower limit of modal class,

l = 46, h = 2, f_{1}, = 14, f_{0} = 5, f_{2} = 4

We know that,

Mode

= l + (\frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}}) \times h

= 46 + (\frac{14 - 5}{2 ( 14 ) - 5 - 4}) \times 2

= 46 + \frac{9}{19} \times 2

= 46 + 0.95

Mode

= 46.95

, verified.

Question Text	During the medical check-up of $35$ students of a class, their weights were recorded as follows: Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

Practice questions from similar books

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