Class 10th, Statistics, 14.4 (Solution)

Class 10th,- Statistics

 Exercise: 14.4 (Solution), Q1 to Q3

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Q1. The following distribution gives the daily income of 50 workers if a factory. Convert the distribution above to a less than type cumulative frequency distribution and draw its ogive.

Daily income in Rupees	100-120	120-140	140-160	160-180	180-200
Number of workers	12	14	8	6	10

Solution:- Convert the given distribution table to a less than type cumulative frequency distribution, and we get

Daily income	Frequency	Cumulative Frequency
Less than 120	12	12
Less than 140	14	26
Less than 160	8	34
Less than 180	6	40
Less than 200	10	50

From the table plot the points corresponding to the ordered pairs such as (120, 12), (140, 26), (160, 34), (180, 40) and (200, 50) on graph paper and the plotted points are joined to get a smooth curve and the obtained curve is known as less than type ogive curve

Q2. During the medical check-up 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 give for the given data.
Hence obtain the median weight from the graph and verify the result by using the formula.
Solution: From the given data, to represent the table in the form of graph, choose the upper limits of the class intervals are in x-axis and frequencies on y-axis by choosing the convenient scale.

Now plot the points corresponding to the ordered pairs given by (38, 0), (40, 3), (42, 5), (44, 9),(46, 14), (48, 28), (50, 32) and (52, 35) on a graph paper an join them to get a smooth curve. The curve obtained is known as less than type give.

Locate the point 17.5 on the y-axis and draw a line parallel to the x-axis cutting the curve at a point. From the point, draw a perpendicular line to the x-axis.
The intersection point perpendicular to x-axis is the median of the given data.
Now, to find the mode by making a table.

Class interval	Number of students(Frequency)	Cumulative Frequency
Less than 38	0	0
Less than 40	3-0=3	3
Less than 42	5-3=2	8
Less than 44	9-5=4	9
Less than 46	14-9=5	14
Less than 48	28-14=14	28
Less than 50	32-28=4	32
Less than 52	35-22=3	35

Q3. The following tables gives production yield per hectare of wheat of 100 farms of a village.

Production Yield	50-55	55-60	60-65	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 its ogive.
Solution: converting the given distribution to a more than type distribution, we get

Production Yield (kg/ha)	Number of farms
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

From the table obtained draw the give by plotting the corresponding points where the upper limits in x-axis and the frequencies obtained in the y-axis are (50, 100), (55, 98), (60, 90), (65, 78), (70, 54) and (75, 16) on this graph paper. The graph obtained is known as more than type ogive curve.

See next blog for more solution...... Thank you.