JAC Class 10 Maths Solutions Chapter 14 Statistics Ex 14.4

Jharkhand Board JAC Class 10 Maths Solutions Chapter 14 Statistics Ex 14.4 Textbook Exercise Questions and Answers.

JAC Board Class 10 Maths Solutions Chapter 14 Statistics Exercise 14.4

Question 1.
The following distribution gives the daily income of 50 workers of a factory:
JAC Class 10 Maths Solutions Chapter 14 Statistics Ex 14.4 1
Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.
Solution:
JAC Class 10 Maths Solutions Chapter 14 Statistics Ex 14.4 2
JAC Class 10 Maths Solutions Chapter 14 Statistics Ex 14.4 3

JAC Class 10 Maths Solutions Chapter 14 Statistics Ex 14.4

Question 2.
During the medical check-up of 35 students of a class, their weights were recorded as follows:

Weight (in kg)No. of students
Less than 380
Less than 403
Less than 425
Less than 449
Less than 4614
Less than 4828
Less than 5032
Less than 5235

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.
Solution:

Weight (in kg)FrequencyCumulative frequency
36 – 3800
38 – 4033
40 – 4225
42 – 4449
44 – 46514 = cf
46 – 4814 = f28
48 – 50432
50 – 52335
n = 35

\(\frac{\mathrm{n}}{2}=\frac{35}{2}=17.5\)
Plot the points (38, 0) (40, 3) (42, 5) (44, 9) (46, 14) (48, 28) (50, 32) (52, 35)
Median = l + \(\left[\frac{\frac{\mathrm{n}}{2}-\mathrm{cf}}{\mathrm{f}}\right]\) × h
= 46 + \(\left[\frac{17.5-14}{14}\right]\) × 2
= 46 + \(\frac{3.5 \times 2}{14}\)
= 46 + 0.5= 46.5.
JAC Class 10 Maths Solutions Chapter 14 Statistics Ex 14.4 4

JAC Class 10 Maths Solutions Chapter 14 Statistics Ex 14.4

Question 3.
The following table gives production yield per hectare of wheat of 100 farms of a village:
JAC Class 10 Maths Solutions Chapter 14 Statistics Ex 14.4 5
Change the distribution to a more than type distribution, and draw its ogive.
Solution:

Production yield (in kg/hec)Number of farmsc.f.
More than 502100
More than 55898
More than 601290
More than 652478
More than 703854
More than 751616

∴ Co-ordinate points are (50, 100), (55, 98), (60, 90), (65, 78), (70, 54) and (75, 16).
JAC Class 10 Maths Solutions Chapter 14 Statistics Ex 14.4 6

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