Calculate mode from the following series:

Size 1 2 3 4 5 6 7 8 9 10

Frequency 8 6 10 12 20 12 5 3 2 4

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Solution

The data given in the question is a discrete series. Therefore, using the inspection method of ascertaining mode, we know that the item which repeats itself the maximum number of times is regarded as the mode of the given series. In this manner, 5 is regarded as the modal value, as it has the highest frequency (of 20 times).
Therefore, mode (Z) is 5.

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Size of Items	3−4	4−5	5−6	6−7	7−8	8−9	9−10
Frequency	3	7	22	60	85	32	9

Size	0−4	4−6	6−10	10−15	15−20	20−30	30−35	35−40
Frequency	2	4	3	5	2	20	6	8

x_i	5	7	9	10	12	15
f_i	8	6	2	2	2	6

x_i	5	10	15	20	25
f_i	7	4	6	3	5

x_i	10	30	50	70	90
f_i	4	24	28	16	8

Size	20	21	22	23	24
Frequency	6	4	5	1	4

Size	1	3	5	7	9	11	13	15
Frequency	3	3	4	14	7	4	3	4

Class	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	2	4	6	8	6	4	2

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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