Question

The median of 27 observations of a variable is 18. Three more observations are made, and the values of these observations are 16, 18 and 50. What is the median of these 30 observations?
1. 18
2. 19
3. 25.5
4. 26

Answer 1

Correct Answer - Option 1 : 18

Median of 27 observations = 18

Then, \({\left( {\frac{{27 + 1}}{2}} \right)^{{\rm{th}}}}\) observation = 18

and 14^th observation = 18

Then, observation whose value is 16 come before 18, i.e., 14^th observation.

Now, number of observations is even 30 observations.

\(Median = \frac{{\left( {{{\left( {\frac{{30}}{2}} \right)}^{{\rm{th}}}} + {{\left( {\frac{{30}}{2} + 1} \right)}^{{\rm{th}}}}} \right)}}{2}\) 

\(= \frac{{15th\;observation + 16th\;observation}}{2}\)

\(= \frac{{18 + 18}}{2} = 18\)