Mode

The mode of a set of data is that value which occurs most often.

Example 3.8: The mode of the following simple discrete frequency distribution . . .

X	4	5	6	7	8	9	10
F	2	5	21	18	9	2	1

is 6, since this value has the largest frequency.

The Mode for Grouped Data

^Mode 

Where 

l = lower boundary of the modal class

i = modal class width

D₁ = difference between largest frequency and the frequency immediately preceding it.

D₂ = difference between the largest frequency and the frequency immediately following it.

Example 3.9: Estimate the mode of the following distributions:

Age (years)	Number of Employees
20 and < 25	2
25 and < 30	14
30 and < 35	29
35 and < 40	43
40 and < 45	33
45 and < 50	9

Here modal class is 35 and <40 and therefore

l =35

i = 5

D₁ = 43-29 = 14

D₂ = 43-33 = 10

^{Thus mode}   

By Graphical Estimation:

The procedure is to construct a histogram and identify the highest bar.  Join the corner points as shown below:

Example 3.10: Estimate the mode graphically of the distribution in the example above on age of employees.

Age (years)	f	Class Width	Frequency Density
20 - < 25	2	5	0.4
25 - < 30	14	5	2.8
30 - < 35	29	5	5.8
35 - < 40	43	5	8.6
40 - < 45	33	5	6.6
45 - < 50	9	5	1.8