Calculate mode of the following series:

Class Interval 0−5 5−10 10−15 15−20 20−25 25−30

Frequency 20 24 32 28 20 26

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Solution

Class Interval Frequency

0 − 5
5 − 10
(l₁)10 − 15
15 − 20
20 − 25
25 − 30 20
24 f₀
32 f₁
28 f₂
20
26

A glance at the series reveal that 10 − 15 is the modal class because it has the maximum frequency i.e. 32. Therefore,the modal value will be:

$Z = l_{1} + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times i or, Z = 10 + \frac{32 - 24}{2 (32) - 24 - 28} \times 5 or, Z = 10 + \frac{8}{64 - 52} \times 5 or, Z = 10 + \frac{40}{12} or, Z = 10 + 3.33 \Rightarrow Z = 13.33$

Hence, the Mode (Z) of the above series is 13.33

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Similar questions

Calculate mode from following data:

$\begin{matrix} Class Interval & 5 - 14 & 15 - 24 & 25 - 34 & 35 - 44 & 44 - 54 & 55 - 64 Frequency & 8 & 10 & 15 & 25 & 40 & 20 \end{matrix}$ .

Class-Interval	0−5	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Frequency	5	7	15	18	16	9	6	3

Size	0−5	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Frequency	2	5	7	13	21	16	8	3

Wage Rate (₹)	25−30	20−25	15−20	10−15	5−10	0−5
Number of Workers	5	10	20	5	8	2

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Class Interval	Frequency
0 − 5 5 − 10 (l₁)10 − 15 15 − 20 20 − 25 25 − 30	20 24 f₀ 32 f₁ 28 f₂ 20 26

Class Interval	0−5	5−10	10−15	15−20	20−25	25−30
Frequency	20	24	32	28	20	26