Calculate mode from the following data-Wages - Number of Workers Less than 10 15 Less than 20 35 Less than 30 60 Less than 40 84 Less than 50 96 Less than 60 127 Less than 70 198 Less than 80 250

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Mode of Continuous Series

Calculate mod...

Question

Calculate mode from the following data:

Wages (₹) Number of Workers

Less than 10
Less than 20
Less than 30
Less than 40
Less than 50
Less than 60
Less than 70
Less than 80 15
35
60
84
96
127
198
250

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Solution

To calculate the value of mode, we first convert the given less than cumulative frequency distribution into a simple frequency distribution as follows.

Wages No. of Wages
(f)

0 − 10
10 − 20
20 − 30
30 − 40
40 − 50
50 − 60
60 − 70
70 − 80 15
35 − 15 = 20
60 − 35 = 25
84 − 60 = 24
97 − 84 = 12
127 − 96 = 31(f₀)
198 − 127 = 71 (f₁)
250 − 198 = 52 (f₂)

By inspection, we can say that the modal class is 60 – 70 as it has the highest frequency of 71.
$Mode (Z) = l_{1} + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times i or, Z = 60 + \frac{71 - 31}{2 (71) - 31 - 52} \times 10 or, Z = 60 + \frac{40}{142 - 83} \times 10 or, Z = 60 + \frac{400}{59} or, Z = 60 + 6.78 = 66.78 Hence, Mode is 66.78$

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Wages (₹)	Number of Workers
Less than 10 Less than 20 Less than 30 Less than 40 Less than 50 Less than 60 Less than 70 Less than 80	15 35 60 84 96 127 198 250

Wages	No. of Wages (f)
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80	15 35 − 15 = 20 60 − 35 = 25 84 − 60 = 24 97 − 84 = 12 127 − 96 = 31(f₀) 198 − 127 = 71 (f₁) 250 − 198 = 52 (f₂)

Calculate mode from the following data: Wages (₹) Number of Workers Less than 10 Less than 20 Less than 30 Less than 40 Less than 50 Less than 60 Less than 70 Less than 80 15 35 60 84 96 127 198 250

Calculate mode from the following data:

Wages (₹) Number of Workers

Less than 10
Less than 20
Less than 30
Less than 40
Less than 50
Less than 60
Less than 70
Less than 80 15
35
60
84
96
127
198
250