Question

A football player scored the following number of goals in the 10 matches.
1, 3, 2, 5, 8, 6, 1, 4, 7, 9.
Since the number of matches is 10 (an even number), therefore the median is $=\dfrac{{{5}^{th}}\text{ observation + }{{\text{6}}^{th}}\text{ observations}}{2}$
$=\dfrac{8+6}{2}=7$
Is this the correct Answer.
$\begin{align}
  & \text{a) correct}\text{.} \\
 & \text{b) incorrect}\text{.} \\
 & \text{c) ambiguous}\text{.} \\
 & \text{d) data insufficient}\text{.} \\
\end{align}$

Answer 1

Hint:The median of a set of numbers is the middle number in the set after the numbers are arranged in ascending order. Now if there are even number of data then the mean is the average of the middle two terms

Complete step by step answer:
Now the given data is 1, 3, 2, 5, 8, 6, 1, 4, 7, 9.
Now know that the median of data is the middle number in the data after the data is arranged in ascending order that is from lowest to highest number. Now if there are even numbers of data then the mean is given by taking an average of the middle two terms and if there is the odd number of data then the mean is given by ${{\dfrac{\left( n+1 \right)}{2}}^{th}}$ term.
Hence to take the median of the data let us first arrange the terms in ascending order.
Arranging in ascending order we get 1, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Now there are 10 numbers and we know that 10 is an even number
Hence the median is the mean of the middle two terms
Now middle two terms are 5th term and 6th term which are 4 and 5
Hence the median will be mean of 4 and 5
Hence the median is $\dfrac{4+5}{2}=\dfrac{9}{2}=4.5$
Hence the median is 4.5.
Now in the given question, their median is 7.
Hence the answer is not correct.
Hence option b is the correct option.

Note:
 Note that while taking the median we first need to list the numbers in ascending. Once the numbers are in ascending order then only we can calculate the median.