The following table gives the lifetime in days of $100$ electricity tubes of a certain make:

Find the mean lifetime of electricity tubes by the step deviation method.

The correct option is A: $145$

$d=\frac{x-A}{h}$

For class interval $0-50,\Rightarrow d=\frac{25-175}{50}=-3$

Assumed mean, $A=175$

class size, $h=50$

total frequency $=N=100$

Actual mean, $\overline{x}=A+\frac{\sum fd}{N}\times h$

$=175+\frac{-60}{100}\times 50$

$=175-30$

$=145$