The following data gives the information on the observed lifetimes (in hours) of 225 electrical components :

Lifetime (in hours)	Frequency
0 - 20	10
20 - 40	35
40 - 60	52
60 - 80	61
80 - 100	38
100 - 120	29

Determine the modal lifetimes of the components.

By formula,

Mode = l + $\Big(\dfrac{f$1 - f0}{2f1 - f0 - f_2}\Big) \times h

Here,

1. Class size is h.

2. The lower limit of modal class is l

3. The Frequency of modal class is f₁.

4. Frequency of class preceding modal class is f₀.

5. Frequency of class succeeding the modal class is f₂.

Class 60 - 80 has the highest frequency.

∴ It is the modal class.

∴ l = 60, f₁ = 61, f₀ = 52, f₂ = 38 and h = 20.

Substituting values we get :

$\text{Mode} = 60 + \Big(\dfrac{61 - 52}{2 \times 61 - 52 - 38}\Big) \times 20 \\[1em] = 60 + \dfrac{9}{122 - 90} \times 20 \\[1em] = 60 + \dfrac{180}{32} \\[1em] = 60 + 5.625 \\[1em] = 65.625$

Hence, modal lifetime = 65.625 hours.