Question

find the value of x from the following data if its mode is 65.

class. frequency. 0 - 20. 6. 20-40. 8. 40-60. x. 60-80. 12. 80-100. 6. 100-120. 5​

Answer 1

Step-by-step explanation:

Given Find the value of x from the following data if its mode is 65.class. frequency. 0 - 20. 6. 20-40. 8. 40-60. x. 60-80. 12. 80-100. 6. 100-120. 5

•            Class                       Frequency
•         0 – 20                              6
•         20 – 40                            8
•          40 – 60                           x
•          60 – 80                           12
•          80 – 100                          6
•        100 – 120                          5
• So we have Mode = l + (f1 – fo / 2f1 – fo – f2) x h
•                      65 = 60 + (12 – x / 2(12) – x – 6) x 20 (h is size)
•                          5 = (12 – x / 18 – x) x 20
•                  5/20 = 12 – x / 18 – x
•                   ¼ = 12 – x / 18 – x
•                  18 – x = 48 – 4x
•                      3x = 30
•                      x = 30 / 3
•                      Or x = 10

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Answer 2

Solution :-

Class frequency

0-20 6

20-40 8

40-60 x

60-80 12

80-100 6

100-120 5

we know that :-

Mode = L + {(f1 - f0) / (2f1 - f0 - f2)} * h

we have :-

• Mode = 65
• L = 60
• f1 = 12
• f0 = x
• f2 = 6
• h = 20

Putting all values we get :-

→ 65 = 60 + {(12 - x) / (2 * 12 - x - 6)} * 20

→ 65 - 60 = 20(12 - x) / (18 - x)

→ 5(18 - x) = 20(12 - x)

→ 18 - x = 4(12 - x)

→ 18 - x = 48 - 4x

→ 4x - x = 48 - 18

→ 3x = 30

→ x = 10 (Ans.)

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