Question

Calculate the median for the following distribution class

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	5	10	20	7	8	5

Answer 1

Hint:
Here we will first make the table including cumulative frequency. Then we will find the median class from the given data. Then we will find the lowest limit, the frequency of the median class, width of the class and the total frequency before the median class. We will then put these obtained values in the formula of the median to find its value.

Formula used:
We will use the formula Median \[ = L + \dfrac{{\left( {n/2} \right) - B}}{F} \cdot W\] where, \[L\] is the lowest limit of the median class, \[n\] is the total frequency of the data, \[B\] is the total frequency before the median class, \[F\] is the frequency of the median class, \[W\] is the width of the class.

Complete Step by Step Solution:
Firstly we will make the table with the cumulative frequency. Therefore, we get

Class	Frequency	Cumulative frequency
0-10	5	5
10-20	10	15
20-30	20	35
30-40	7	42
40-50	8	50
50-60	5	55

So from the table we get a total frequency equal to 55 i.e. \[n = 55\].
Now we will find the class in which the median will lie. Therefore we will find the value of \[\dfrac{n}{2}\] and find the class where it lies, we get
\[\therefore \dfrac{n}{2}=\dfrac{55}{2}=27.5\]
From the table we can see that \[27.5\] lies in the class 20-30.
Hence the median class is 20-30.
Now we will use the formula of the median to calculate the value of the median. Therefore, we get
Lowest limit of the median class is 20 i.e. \[L = 20\]
Total frequency of the data is 55 i.e. \[n = 55\]
Total frequency before the median class is 15 i.e. \[B = 15\]
Frequency of the median class is 20 i.e. \[F = 20\]
Width of the class is 10 i.e. \[W = 10\]
Now we will put all the values in the formula of the median. Therefore, we get
Median \[ = 20 + \dfrac{{\left( {\dfrac{{55}}{2}} \right) - 15}}{{20}} \cdot 10\]
Now by solving this, we will get the value of the median, we get
\[ \Rightarrow \] Median \[ = 20 + 6.25 = 26.25\]

Hence \[26.25\] is the median of the given data.

Note:
We should remember the formula of the median of a data with the frequencies. Here, we should not get confused between mean, median, and mode. Median is the middle value of the given list of numbers or it is the value that is separating the data into two halves i.e. upper half and lower half. A mode is a number or value which occurs a maximum number of times in a given set of numbers. Mean is the average of the given data.
In this question, we might make a mistake by just finding the median class and not the median. So, this will be termed as an incomplete answer.