Answer :

We have been given data of weight in less than type and data of number of students.

We have



Taking weight as x-axis and number of students as y-axis.


Thus plotting the points on a graph, we get



Now we need to plot median in the graph and then verify it using the formula.


So, note that total number of students are 35.


N = 35


Find N/2.




Draw a line parallel to x axis, passing through 17.2 on y-axis intersecting the less than ogive.


We have graphically,



We can notice from the graph, the line intersecting the ogive touches the y-axis at 46.7.


Now, let us solve theoretically,


Let us make a table showing frequencies and class intervals.



Since,


Observe, cf = 28 is just greater than 17.5.


Thus, median class = 46 – 48


Median is given by



Where,


L = Lower class limit of median class = 46


N/2 = 17.5


cf = cumulative frequency of the class preceding median class = 12


f = frequency of the median class = 16


h = class interval of the median class = 2


Substituting these values in the formula of median, we get




Median = 46 + 0.6875


Median = 46.6875


Thus, the median of data is 46.6875 and it is verified.


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