Question

33. Mohan decided to complete his Maths project. He was collected the marks in Maths from two
sections. The total number of students in two sections is 80. After collecting the data, he
analyzed the data and prepared a report on the Maths marks of two sections. Using this report,
he drew the following graph for a particular of Maths marks of two sections:
90
80
-80
80-
64
Number of students
-Curve 1
B
---Curve 2
0
10
20
30
40
70
80
90
100 110
50 60
Marks
Based on the above graph, answer the following questions:
(1) Identify less than type ogive and more than type ogive from the given graph.
(ii) Find the median marks of two sections.
(iii) Obtain the Mode of the data if mean rainfall is 52 cm​

Answer 1

33. Mohan decided to complete his Maths project. He was collected the marks in Maths from two  sections. The total number of students in two sections is 80. After collecting the data, he  analyzed the data and prepared a report on the Maths marks of two sections.

(1) Identify less than type ogive and more than type ogive from the given graph.

The curve 1 is less than ogive

And the curve 2 is more-than ogive.

(As, in less than ogive, the cumulative frequency (cf) increases.

(ii) Find the median marks of two sections.

The point of intersection of less than ogive and more than ogive is the median.

So, we can obtain the median by drawing a perpendicular line from the point of intersection of less than ogive and more than ogive.

Hence we get,

Median marks of two sections  to be 52 cm.

(iii) Obtain the Mode of the data if mean rainfall is 52 cm

As we know that,

3 Median = Mode + 2 Mean

Median = 52 cm

Mean = 52 cm

3 × 52 = Mode + 2 × 52

156 = Mode + 104

Mode = 52 cm