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The Daily Wages of 80 Workers in a Project Are Given Below. - Mathematics

Sum

The daily wages of 80 workers in a project are given below.

Wages
(in Rs.)
400-450 450-500 500-550 550-600 600-650 650-700 700-750
No. of
Workers
2 6 12 18 24 13 5

Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = Rs.
50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate:

1) the median wage of the workers

2) the lower quartile wage of workers

3) the numbers of workers who earn more than Rs. 625 daily

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Solution

The cumulative frequency table of the given distribution is as follows:

Wages in Rs Upper Limit No. of workers Cumulative frequency
400-450 450 2 2
450-500 500 6 8
500-550 550 12 20
550-600 600 18 38
600-650 650 24 62
650-700 700 13 75
700-750 750 5 80

The ogive is as follows:

Number of workers = n = 80

1) Median = (n/2)th term = 40th term

Through mark 40 on the Y-axis, draw a horizontal line which meets the curve at point A.

Through point A, on the curve draw a vertical line which meets the X-axis at point B

The value of point B on the X-axis is the median, which is 605.

2) Lower quartile `(Q_1) = (80/4)th` term = 20th term = 550

3) Through mark of 625 on X-axis, draw a verticle line which meets the graph at point C.

Then through point C, draw a horizontal line which meets the Y-axis at the mark of 50.

Thus, the number of workers that earn more than Rs. 625 daily =  80-50 = 30

Concept: Ogives (Cumulative Frequency Graphs)
  Is there an error in this question or solution?
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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 24 Measure of Central Tendency(Mean, Median, Quartiles and Mode)
Exercise 24 (E) | Q 22 | Page 377
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