Step 1: Find the class mark $x_{i}$ of each class using $x_{i}=\dfrac{\text{lower limit}+\text{upper limit}}{2}$, then compute $f_{i}x_{i}$.
| Lifetime | $f_{i}$ | $x_{i}$ | $f_{i}x_{i}$ |
|---|---|---|---|
| 0-20 | 10 | 10 | 100 |
| 20-40 | 35 | 30 | 1050 |
| 40-60 | 50 | 50 | 2500 |
| 60-80 | 60 | 70 | 4200 |
| 80-100 | 30 | 90 | 2700 |
| 100-120 | 15 | 110 | 1650 |
| <b>Total</b> | <b>200</b> | | <b>12200</b> |
Step 2: Add the frequencies.
$$\sum f_{i}=10+35+50+60+30+15=200$$
Step 3: Add the products.
$$\sum f_{i}x_{i}=100+1050+2500+4200+2700+1650=12200$$
Step 4: Apply the direct method formula for the mean.
$$\bar{x}=\frac{\sum f_{i}x_{i}}{\sum f_{i}}$$
Step 5: Substitute the values.
$$\bar{x}=\frac{12200}{200}=61$$
Hence the mean lifetime of the electrical components is $61$ hours.