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#### A football player scored the following number of goals in the 10 matches: 1, 3, 2, 5, 8, 6, 1, 4, 7, 9Since the number of matches is 10 (an even number), therefore, the median$=\frac{5th\; \text {observation}+6th \; \text {observation}}{2}$$=\frac{8+6}{2}=7$Is it the correct answer and why?

Answer : [No, as the data is not arranged in ascending order before finding the middle terms]

Given terms : 1, 3, 2, 5, 8, 6, 1, 4, 7, 9

To calculate the median, arrange the given data in ascending order and then find the middle term. This middle term is called the median.

Firstly, we will arrange the data in ascending order as:

$1, 1, 2, 3, 4, 5, 6, 7, 8, 9.$

Here the total number of observations, n=10 which is even.

In case of even number of terms:

$\text{Median = average of }( \frac{n}{2} )^{th}$ $\text{ and}$ $\left ( \frac{n}{2}+1 \right )^{th}\text{ term}$

$\text{Median} =\frac{\left ( \frac{n}{2} \right )^{th}observation+\left [ \frac{n}{2}+1 \right ]^{th}observation}{2}$

$\Rightarrow \frac{\left ( \frac{10}{2} \right )^{th}observation+\left [ \frac{10}{2}+1 \right ]^{th}observation}{2}$

$\Rightarrow \frac{5^{th}\; \text {observation}+6^{th}\text {observation}}{2}$

$\Rightarrow \frac{4+5}{2}=\frac{9}{2}=4.5$

Hence, the median is 4.5