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NCERT TEXTBOOK QUESTIONS SOLVED
Page No. 293
EXERCISE 14.4
Q 1. The following distribution gives the daily income of 50 workers of a factory
Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.
Sol. We have the cumulative frequency distribution as:
Daily income (in Rs )  Cumulative frequencies 
Less than 120  12 + 0 = 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 
Now, we plot the points corresponding to the ordered pairs (120, 12), (140, 26), (160, 34), (180, 40) and (200, 50) on a graph paper and join them by a free hand smooth curve as shown below:
The curve so obtained is called the less than o give.
Q 2. During the medical checkup of 35 students of a class, their weights were recorded as follows:
Weight (in kg)  Number of students 
Less than 38  0 
Less than 40  3 
Less than 42  5 
Less than 44  9 
Less than 46  14 
Less than 48  28 
Less than 50  32 
Less than 52  35 
Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula
Sol. Here, the values 38, 40, 42, 44, 46, 48, 50 and 52 are the upper limits of the respective class intervals.
We plot the points (ordered pairs) (38, 0), (40, 3), (42, 5), (44, 9), (46, 14), (48, 28), (50, 32) and (52, 35) on a graph paper and join them by a free hand smooth curve.
The curve so obtained is the less than type ogive.
∵ n = 35
The point 17.5 is on yaxis.
From this point (i.e., from 17.5) we draw a line parallel to the xaxis which cuts the curve at P. From this point (i.e., from P), draw a perpendicular to the xaxis, meeting the xaxis at Q. The point Q represents the median of the data which is 47.5.
Verification
To verify the result using the formula, let us make the following table in order to find median using the formula:
Weight (in kg)  Number of students [Cumulative frequency] 
038  0 
3840  3 
4042  5 
4244  9 
4446  14 
4648  28 
4850  32 
5052  35 
Here,
Since, this observation lies in the class 46 − 48.
∴ The median class is 46 − 48 such that l = 46, h = 2, f = 14, cf = 14
Thus, the median = 46.5 kg is approximately verified.
Q 3. The following table gives production yield per hectare of wheat of 100 farms of a village.
Production yield (in kg/ha)  5055  5560  6065  6570  7075  7580 
Number of farms  2  8  12  24  38  16 
Change the distribution to a more than type distribution, and draw its ogive.
Sol. For ‘more than type’ distribution, we have:
Production yield (in kg/ha)  Number of farms (Cumulative frequencies) 
More than 50  100 
More than 55  98 
More than 60  90 
More than 65  78 
More than 70  54 
More than 75  16 
Now, we plot the points (50, 100), (55, 98), (60, 90), (65, 78), (70, 54) and (75, 16) and join the points with a free hand curve.
The curve so obtained is the ‘more than type ogive’.
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