Question

Find the median of the following observations: $46,64,87,41,58,77,35,90,55,92,33$.

If $92$ is replaced by $99$ and $41$ by $43$ in the above data, find the new median.

Answer 1

Find the median and new median:

The observations are $46,64,87,41,58,77,35,90,55,92,33$.

Let $n$ be the number of observations, $n=11$

We have to write the observations in ascending order: $33,35,41,46,55,58,64,77,87,90,92$

When $n$ is odd, then median $=\frac{1}{2}\left(n+1\right)thterm$

$$\begin{gathered} =\frac{1}{2}\left(11+1\right)thterm \\ =\frac{1}{2}\left(12\right)thterm \\ =6thterm \end{gathered}$$

Therefore, the median is $58$.

If $92$ is replaced by $99$ and $41$ by $43$ then the above observations will be written as $33,35,43,46,55,58,64,77,87,90,99$.

Hence, the new median is also $58$.

Final answer: The median and new median is $58$.