Find out the mode value from the following data:

Mid-value 15 25 35 45 55 65 75 85

Frequency 5 8 12 16 28 15 3 2

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Solution

Mid Value Class Interval Frequency
(f)

15
25
35
45
55
65
75
85 10 − 20
20 − 30
30 − 40
40 − 50
50 − 60
60 − 70
70 − 80
80 − 90 5
8
12
16 f₀
28 f₁
15 f₂
3
2

By inspection, we can say that the modal class is (50 – 60) as it has the highest frequency of 28.
$Mode (Z) = l_{1} + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times i or, Z = 50 + \frac{28 - 16}{2 (28) - 16 - 15} \times 10 or, Z = 50 + \frac{12}{25} \times 10 or, Z = 50 + 4.8 = 54.8 Hence, mode (Z) is 54.8 .$

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Mid Value	Class Interval	Frequency (f)
15 25 35 45 55 65 75 85	10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80 80 − 90	5 8 12 16 f₀ 28 f₁ 15 f₂ 3 2

Find out the mode value from the following data: Mid-value 15 25 35 45 55 65 75 85 Frequency 5 8 12 16 28 15 3 2

Find out the mode value from the following data:

Mid-value 15 25 35 45 55 65 75 85

Frequency 5 8 12 16 28 15 3 2