Question

The mode of the following data is 33 1/3 and the total frequency is 100:
Class. Frequency
0 - 10. 7
10 - 20. 12
20-30. x
30-40. 28
40-50. y
50-60. 9
Find the missing frequencies x and y.
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Answer 1

Step-by-step explanation:

Given The mode of the following data is 33 1/3 and the total frequency is 100:

Class. Frequency

0 - 10. 7

10 - 20. 12

20-30. x

30-40. 28

40-50. y

50-60. 9

Find the missing frequencies x and y.  

• So ∑ f1 = 100
• So we get by adding
•       56 + x + y = 100
•          Or x = 44 – y ---------1
• So the Modal Class is 30 – 40
• Now l = 30, fo = x, f1 = 28, f2 = y, h = 10
• So Mode = 33 1/3
• So l + f1 – fo / 2f1 – fo – f2 x h = 100 / 3
•      30 + 28 – x / 2 x 28 – x – y x 10 = 100 / 3
•       30 + 28 – (44 – y) / 56 – (44 – y) – y x 10 = 100 / 3
•                 28 – 44 + y / 56 – 44 + y – y x 10 = 3.33
•                     y – 16 / 12  x 10 = 3.33
•                     (y – 16) 5 = 3.33 x 6
•                    5y – 80 = 19.98
•                      5y = 99.98
•                   Or y = 19.99
•  Substituting y in equation 1 we have,
•                       x = 44 – 19.99
•                       x = 24.01

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Answer 2

Answer:

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