The following frequency distribution showing the marks obtained by 100 students in Math. Find the median.

# The following frequency distribution showing the marks obtained by students in Math. Find the median.

1. A
$40$
2. B
$50$
3. C
$60$
4. D
$70$

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### Solution:

The following frequency distribution showing the marks obtained by students in Math:
From the given table, we have the frequency distribution table as,
We have,
N $=100$ We know,
Here, the cumulative frequency just greater than 50 is 78 and the corresponding class is
Therefore, the median class is
The general formula for median is given as,
Median $=l+\frac{\frac{N}{2}-C.F.}{f}×h$ Where,
l = lower limit of median class $=40.$
C.F. = C.F. of previous class $=50.$
f = frequency of median class $=50.$
h = width of median class = upper limit - lower limit
$⇒h=50-40$ $⇒h=10$ Substitute in formula, we have,
Median $=40+\left(\frac{\frac{100}{2}-50}{50}\right)×10$  $⇒\mathit{Median}=40+\left(\frac{50-50}{50}\right)×10$  $⇒\mathit{Median}=40+0$  $⇒\mathit{Median}=40$ Therefore, the median value is 40.
Hence, option (1) is correct.
$\mathit{Median}=40+\left(\frac{50-50}{50}\right)×10$  $⇒\mathit{Median}=40+0$  $⇒\mathit{Median}=40$ Therefore, the median value is 40.
Hence, option (1) is correct.

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