The mode calculation steps are as shown below:
1)By preparing a group table and analysis table or by inspection ascertain the model class.
2)Determine the value of the mode by applying the following formula
Mo = L + Δ1 / Δ1 + Δ2 xi
Where,
L = lower limit of the modal class;
Δ1 = the difference b/w the frequency of the modal class & the frequency of the premodal class, preceding clas
|f1 - f0 | : Δ2 = the difference b/w the frequency of the modal class
I = the class interval of the modal class.
The another type of this formula is:
Mo = L + (f1 - f0)/2 (f1 - f0) - (f1 x i)
Where,
L = lower limit of the modal class;
f1 = frequency of the modal class;
f0 = frequency of the class preceding the modal class;
f2 = frequency of the class succeeding the modal class.
Where mode is ill-defined, its value may be ascertained by the following formula depend upon the relationship between mean, median and mode;
Mode = 3 median - 2 mean
This measure is called the empirical mode.
Illustration: - find the value of mode from the data given below:
| Weight (kg) |
No. of students |
Weight (kg) |
No. of students |
| 39-97 |
2 |
113-117 |
14 |
| 98-102 |
5 |
118-122 |
6 |
| 103-107 |
12 |
123-127 |
3 |
| 108-112 |
17 |
128-132 |
1 |
Solution: - by inspection mode lies in the class 108-112, but the real limits of this class are 107, 5-112.5
Mode = L + Δ1 / Δ1 + Δ2 x 1
L = 107.5, Δ1 = f1 – fo = (17 – 12) = 5
Δ2 = f1 – f2 = (17 – 14) = 3, I = 5
Mode = 107, 5 + 5 / 5+3 x5 = 107, 5 + 3,125 = 110.625
Thus the modal weight is 110.625 kg.