Question

Find the median of $17,\,15,\,9,\,13,\,21,\,7,\,32$.

Answer 1

Hint: When we have to find the median of the given data firstly we have to arrange the data in increasing or decreasing order. If there in $n$ terms in the given data and $n$ is odd number then the median of the given data is given by ${\left( {\dfrac{{n + 1}}{2}} \right)^{th}}$ term. And if $n$ is even number then the median of the given data is given by the mean of ${\left( {\dfrac{n}{2}} \right)^{th}}$ term and ${\left( {\dfrac{n}{2}} \right)^{th}} + 1$ terms.

Complete step-by-step answer:
Here, the given data is $17,\,15,\,9,\,13,\,21,\,7,\,32$
Arranging them in increasing order we get,
$7,9,13,15,17,21,32$
The numbers of terms in this data is $7$ which is an odd number.
Since $n$ is an odd number we have to find the median using the formula median $ = {\left( {\dfrac{{n + 1}}{2}} \right)^{th}}$term.
$ \Rightarrow {\left( {\dfrac{{n + 1}}{2}} \right)^{th}} = {\left( {\dfrac{{7 + 1}}{2}} \right)^{th}} = {\left( 4 \right)^{th}}$ term.
The median of the given data is equal to the value of ${\left( 4 \right)^{th}}$ term.
Here, ${\left( 4 \right)^{th}}$ term is $15$.

Thus, the median of the given data is $15$.

Note: Median of the given data is the value of ${\left( {\dfrac{{n + 1}}{2}} \right)^{th}}$ terms is not the value of $\left( {\dfrac{{n + 1}}{2}} \right)$.
Mean, median and mode are the measure of the central tendency of any raw data. Similarly mode is calculated by arranging data in increasing or decreasing order then the mode of the given data is the number from the data which has repeated the maximum number of times. Mean of the raw data is simply the average of the data that is the sum of all data divided by the number of data.
There is an important relationship between mean, median and mode which is given by
Mode$ = 3$Median $ - 2$Mean.