The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observation in the data:\
Given: Median = 525
We prepare the cumulative frequency table, as given below.
Now, we have
$N=100$
$76+f_{1}+f_{2}=100$
$f_{2}=24-f_{1}$....(1)
So, $\frac{N}{2}=50$
Since median $=525$ so the median class is $500-600$.
Here, $l=500, f=20, F=36+f_{1}$ and $h=100$
We know that
Median $=l+\left\{\frac{\frac{N}{2}-F}{f}\right\} \times h$
$525=500+\left\{\frac{50-\left(36+f_{1}\right)}{20}\right\} \times 100$
$25=\frac{\left(14-f_{1}\right) \times 100}{20}$
$25 \times 20=1400-100 f_{1}$
$100 f_{1}=1400-500$
$f_{1}=\frac{900}{100}$
$=9$
Putting the value of $f_{1}$ in (1), we get
$f_{2}=24-9$
$=15$
Hence, the missing frequencies are 9 and 15.