Ex.14.4 Q1 STATISTICS Solution - NCERT Maths Class 10

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Question

The following distribution gives the daily income of  \(50\) workers of a factory.

Daily income (in Rs) \(100 - 120\) \(120 - 140\) \(140 - 160\) \(160 – 180\) \(180 - 200\)
Number of workers \(12\) \(14\) \(8\) \(6\) \(10\)

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

Text Solution

What is known?

The daily income of \(50\) workers of a factory.

What is unknown?

The less than type cumulative frequency distribution and its ogive.

Reasoning:

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

Steps:

The frequency distribution table of less than type is as follows:

Daily income (in Rs) (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 \(200\) \(40 + 10 = 50\)

Taking upper class limits of class intervals on \(x\)-axis and their respective frequencies on \(y\)-axis, its ogive can be drawn as follows:

  
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