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Calculate the median from the following data: Marks 0 – 10 10 – 30 30 – 60 60 – 80 80 – 90 Number of students 5 15 30 8 2
The median is the middle value of the sorted data set, obtained after arranging the data in ascending order.
Answer: The median for the given data is 40.
Let's understand how to find the median for a grouped data.
Explanation:
We need to calculate the cumulative frequencies to find the median.
Marks | Number of students | Cumulative frequency | |
0 - 10 | 5 | 0 + 5 | 5 |
10 - 30 | 15 | 5 + 15 | 20 |
30 - 60 | 30 | 20 + 30 | 50 |
60 - 80 | 8 | 50 + 8 | 58 |
80 - 90 | 2 | 58 + 2 | 60 |
N = \(\sum f_i\) = 60
N/2 = 60/2 = 30
Median Class is 30-60
l = 30, f = 30, c.f = 20, h = 30 \(\)
Using Median formula:
\begin{align}\text { Median } &=l + [\dfrac {\dfrac{n}{2}-c}{f}]\times h\\\\&=30 + \dfrac{30-20}{30} \times 30 \\\\&= 30 + \dfrac{10}{30} \times 30 \\\\&=30+10\\\\\text { Median }&= 40 \end{align}
Thus, the median for the data: Marks 0 – 10, 10 – 30, 30 – 60, 60 – 80 and 80 – 90 Number of students 5,15, 30, 8 and 2 is 40.
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