Question

Compute the mode from the following by: (i) Observation Method; (ii) Grouping Method.

Hight (in inches)	60	62	63	64	65	66	67	68	69	70
No. of Persons	5	13	18	20	21	30	23	12	4	2

Answer 1

(i) Observation Method

Height (X)	No. of persons (f)
60 62 63 64 65	5 13 18 20 21
66	30	Modal Class
67 68 69 70	23 12 4 2

Using the observation 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,66 is regarded as the modal value, as it has the highest frequency (of 30 times).
Therefore, mode (Z) is 66 inches.

(ii) Grouping Method

For the given distribution, the grouping table is as follows.





On the basis of this grouping table, an analysis table is prepared. For each column of the grouping table, we analyse which item/group of items correspond to the highest frequency.

Analysis Table

Column	60	62	63	64	65	66	67	68	69	70
I II III IV V VI VII				✓	✓ ✓ ✓ ✓	✓ ✓ ✓ ✓ ✓ ✓ ✓	✓ ✓ ✓ ✓	✓ ✓
				1	4	7	4	2

From the analysis table, it is clear that 66 repeats the maximum number of times. Thus, mode is 66.