The following table gives the distribution of the life time of 400 neon lamps:
Find the median life.
We prepare the cumulative frequency table, as given below.
We have, $N=400$
So, $\frac{N}{2}=200$
Now, the cumulative frequency just greater than 200 is 216 and the corresponding class is $3000-3500$.
Therefore, $3000-3500$ is the median class.
Here, $I=3000, f=86, F=130$ and $h=500$
We know that
Median $=l+\left\{\frac{\frac{N}{2}-F}{f}\right\} \times h$
$=3000+\left\{\frac{200-130}{86}\right\} \times 500$
$=3000+\frac{70 \times 500}{86}$
$=3000+\frac{35000}{86}$
$=3000+406.98$
$=3406.98$
Hence, the median life of the lamps is approximately 3406.98 hours.
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