Ex.14.4 Q3 STATISTICS Solution - NCERT Maths Class 10

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Question

The following table gives production yield per hectare of wheat of \(100\) farms of a village.

Production yield(in kg/ha) \(50\)\(55\) \(55 \)\(60\) \(8\)\(65\) \(65\)\(70\) \(70\)\(75\) \(75\)\(80\)
Number of farms \(2\) \(8\) \(12\) \(24\) \(38\) \(16\)

Change the distribution to a more than type distribution and draw ogive.

Text Solution

 

What is known?

Production yield per hectare of wheat of \(100\) farms of a village.

What is unknown?

The more than type distribution and its ogive.

Reasoning:

The representation of cumulative frequency distribution graphically is known as a cumulative frequency curve or an ogive.

Steps:

The cumulative frequency distribution of more than type can be obtained as follows.

Production Yield (in kg/ha)

(Lower class limits)

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 \(75\) \(54 - 38 = 16\)

Taking the lower-class limits on \(x\)-axis and their respective cumulative frequencies on \(y\)-axis, its ogive can be obtained as follows.

  
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