Question

Following is the distribution of the long jump competition, in which 250 students participated. Find the median distance jumped by the students. Interpret the median. 

Distance(m)	0-1	1-2	2-3	3-4	4-5
No of students	40	80	62	38	30

Answer 1

\(\sum f_i\) = 250

Finding Median

Median = I + \(\cfrac{{\frac{n}2-cf}}f\) x h

Here,

\(\cfrac N2\) = \(\cfrac{250}2\) = 125

∴ 2 - 3 is median class

And,

t = 2

h = 1 - 0 = 1

cf = 120

Putting values in formula

Medium = I +  \(\cfrac{{\frac{n}2-cf}}f\) x h 

= 2 + \(\cfrac{125-120}{62}\) x 1

= 2 + \(\cfrac5{62}\)

= 2 + 0.0806  

= 2.0806 

Therefore, Median distance jumped by student is 2.0806 m 

By interpreting the median, 

We observe that 50% of students jump below 2.0806 m and  50%