Question

Find the median weight of the students

Weight in kg	Number of students
40-45	2
45-50	3
50-55	8
55-60	6
50-65	6
65-70	3
70-75	2

Answer 1

Hint: To solve this problem, we need to use the formula for the median in a grouped data. For this, first we have to identify the median class. Then, by using the lower limit of this median class, class interval, cumulative frequency of the class before the median class and frequency of the median class, we can find the median weight of the students.
Formula used:
 $ M = l + \dfrac{{\dfrac{n}{2} - cf}}{f} \times h $ , where, $ M $ is median, $ l $ is lower limit of median class, $ n $ is total number of students, $ cf $ is cumulative frequency of the class before median class, $ f $ is frequency of median class and $ h $ is class interval

Complete step-by-step answer:

Weight in kg	Number of students	Cumulative frequency
40-45	2	2
45-50	3	5
50-55	8	13
55-60	6	19
50-65	6	25
65-70	3	28
70-75	2	30
	$ \sum {{f_i}} = 30 $

First, we will find the median class.
The total number of students $ n = \sum {{f_i}} = 30 \Rightarrow \dfrac{n}{2} = \dfrac{{30}}{2} = 15 $
Therefore, 55-60 is the median class.
Lower limit of median class $ l = 55 $
Cumulative frequency of the class before median class $ cf = 13 $
Frequency of the median class $ f = 6 $
Class interval $ h = 60 - 55 = 5 $
Now, we will put these values in the formula $ M = l + \dfrac{{\dfrac{n}{2} - cf}}{f} \times h $
 $
  M = l + \dfrac{{\dfrac{n}{2} - cf}}{f} \times h \\
   \Rightarrow M = 55 + \dfrac{{15 - 13}}{6} \times 5 \\
   \Rightarrow M = 55 + \dfrac{2}{6} \times 5 \\
   \Rightarrow M = 55 + 1.67 \\
   \Rightarrow M = 56.67 \;
  $
Thus, median weight is $ 56.67\;kg $ .
So, the correct answer is “ $ 56.67\;kg $ .”.

Note: In this type of question, when grouped data is given, the most important and the first step to keep in mind that we need to find the median class. After that, we have determined all the terms used in the formula of median by using this median class. We should also keep in mind that cumulative frequency used in the formula should be taken as the cumulative frequency before the median class.