Compute the median for each of the following data:
(i)
(i)
We prepare the cumulative frequency table, as given below.
Now, we have
$N=100$
So, $\frac{N}{2}=50$
Now, the cumulative frequency just greater than 50 is 65 and the corresponding class is $70-90$.
Therefore, $70-90$ is the median class.
Here, $l=70, f=22, F=43$ and $h=20$
We know that
Median $=l+\left\{\frac{\frac{N}{2}-F}{f}\right\} \times h$
$=70+\left\{\frac{50-43}{22}\right\} \times 20$
$=70+\frac{7 \times 20}{22}$
$=70+6.36$
$=76.36$
Hence, the median is 76.36.
Note: The first class in the table can be omitted also.
(ii)
We prepare the cumulative frequency table, as given below.
Now, we have
$N=150$
So. $\frac{N}{2}=75$
Thus, the cumulative frequency just greater than 75 is 105 and the corresponding class is $110-120$.
Therefore, $110-120$ is the median class.
$l=120, f=45, F=60$ and
$h=-10$ (Because class interval given in descending order)
We know that
Median $=l+\left\{\frac{\frac{N}{2}-F}{f}\right\} \times h$
$=120+\left\{\frac{75-60}{45}\right\} \times(-10)$
$=120-\frac{15 \times 10}{45}$
$=120-\frac{150}{45}$
$=120-3.333$
$=116.67$ (approx)
Hence, the median is 116.67.
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