Calculate mode of the following data:

X Below 5 5−10 10−15 15−20 20−25 25−30 30−35 35−40 Above 40

Y 20 24 32 28 20 16 34 10 8

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Solution

X Frequency
(f)

Below 5
5 − 10 20
24 f₀

10 − 15 32 f₁

15 − 20
20 − 25
25 − 30
30 − 35
35 − 40
above 40 28 f₂
20
16
34
10
8

By inspection, we can say that the modal class is (10 – 15) as it has the highest frequency of 32.
$Mode (Z) = l_{1} + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times i or, Z = 10 + \frac{32 - 24}{2 (32) - 24 - 28} \times 5 or, Z = 10 + \frac{40}{12} or, Z = 10 + 3.33 = 13.33 Hence, mode is 13.33 .$

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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

Calculate mode from following data:

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

Size	5−10	10−15	15−20	20−25	25−30	30−35	35−40	40−45	45−50
Frequency	6	10	18	30	15	12	10	6	4

Class Interval	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Number of Children	4	5	3	2	6	7	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

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X	Below 5	5−10	10−15	15−20	20−25	25−30	30−35	35−40	Above 40
Y	20	24	32	28	20	16	34	10	8