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# The marks obtained by 50 students of class 10 out of 80 marks are given in the following frequency distribution. Find the median.Class0-1010-2020-3030-4040-5050-6060-7070-80Frequency258169532

Last updated date: 15th Jul 2024
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Hint: We will first find the total number of students (N) by summing the frequencies of different classes in the given distribution. Now we will identify the class in which the value $\dfrac{N}{2}$ lies and define that class as Median Class. Now the value of Median is obtained from the below formula
Median $= l + \left[ {\dfrac{{\dfrac{N}{2} - cf}}{f}} \right]h$

The frequency table with cumulative frequency is,
 Class Interval Frequency Cumulative Frequency 0-10 2 2 10-20 5 7 20-30 8 15 30-40 16 31 40-50 9 40 50-60 5 45 60-70 3 48 70-80 2 50

Here the sum of the frequencies is $N = 50$.
Now the value of $\dfrac{N}{2}$ is,
$\Rightarrow \dfrac{N}{2} = \dfrac{{50}}{2} = 25$
The value of $\dfrac{N}{2}$ lies in the interval 30-40.
So, the median class is 30-40.
The lower limit of the median class is,
$\Rightarrow l = 30$
Cumulative frequency of class preceding the median class is,
$\Rightarrow cf = 15$
The frequency of the median class is,
$\Rightarrow f = 16$
The height of the class is,
$\Rightarrow h = 40 - 30 = 10$
Then the value of the median is given by,
Median $= l + \left[ {\dfrac{{\dfrac{N}{2} - cf}}{f}} \right]h$
Substitute the values,
$\Rightarrow$ Median $= 30 + \left[ {\dfrac{{25 - 15}}{{16}}} \right] \times 10$
Subtract the value in the numerator and multiply with 10,
$\Rightarrow$ Median $= 30 + \dfrac{{100}}{{16}}$
Divide numerator by the denominator,
$\Rightarrow$ Median $= 30 + 6.25$
$\therefore$ Median $= 36.25$