Maharashtra State BoardHSC Commerce 11th
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From the following distribution, determine median graphically. Daily Wages (in Rs.) No. of employees Above 300 520 Above 400 470 Above 500 399 Above 600 210 Above 700 105 Above 800 45 Above 900 7 - Mathematics and Statistics

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From the following distribution, determine median graphically.

Daily wages (in ₹) No. of employees
Above 300 520
Above 400 470
Above 500 399
Above 600 210
Above 700 105
Above 800 45
Above 900 7
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Solution 1

The given ‘more than cumulative frequency’ table is,

Daily Wages
(in Rs.)
No. of employee
(m.c.f)
Above 300 520
Above 400 470
Above 500 399
Above 600 210
Above 700 105
Above 800 45
Above 900 7

The ‘more than ogive curve’ is plotted using the given lower limit of the class interval (x) against c.f. (y)
For median draw a line parallel to X-axis at Frequency `"N"/(2) = (520)/(2)` = 260

Solution 2

To draw a ogive curve, we construct the less than and more than cumulative frequency table as given below:

Daily wages (in ₹) No. of employees
(f)
Less than cumulative frequency
(c.f.)
More than cumulative frequency
(c.f.)
300 − 400 50 50 520
400 − 500 71 121 470
500 − 600 189 310 399
600 − 700 105 415 210
700 − 800 60 475 105
800 − 900 38 513 45
900 − 1000 7 520 7
Total 520    

The points to be plotted for less than ogive are (400, 50), (500, 121), (600, 310), (700, 415), (800, 475), (900, 513) and (1000, 520) and that for more than ogive are (300, 520), (400, 470), (500, 399), (600, 210), (700, 105), (800, 45), (900, 7).

From the point of intersection of two ogives, we draw a perpendicular on X-axis.
The point where it meets the X-axis gives the value of the median.
∴ Median ≈ 574

Concept: Concept of Median
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