Question

Calculate the mean and the median of the numbers:$2,1,0,3,1,2,3,4,3,5$

Answer 1

Hint: Question is based on the statistics problem, which is based on the formulas. So in order to calculate the mean and median first we will arrange the numbers in ascending order then simply apply the formula of mean and median, which will give us the answer.

Complete step by step answer:
Moving ahead with the question in a stepwise manner; first arrange the numbers in the ascending order, which is required for using the formula of median and also it helps us to apply other formulas easily. So after arranging the number in ascending order we will get;
$0,1,1,2,2,3,3,3,4,5$
So to find the mean of a arrangement or numbers, we know that mean is the sum of all number/arrangements upon total number of numbers/arrangement i.e.
$\text{mean}=\dfrac{\text{sum }\!\!~\!\!\text{ of }\!\!~\!\!\text{ all }\!\!~\!\!\text{ numbers}}{\text{total }\!\!~\!\!\text{ number }\!\!~\!\!\text{ of }\!\!~\!\!\text{ numbers}/\text{arrangements}}$
So sum of all numbers will be,
$0+1+1+2+2+3+3+3+4+5=24$
Total number of numbers is 10. So mean will be;
$\begin{align}
  & \text{mean}=\dfrac{24}{10} \\
 & \text{mean}=2.4 \\
\end{align}$
For median; first the sequence should be arrange in ascending order, which we had arranged it, now in the arrangement for median we know that;
Median$=\dfrac{1}{2}\left[ {{\left( \dfrac{n}{2} \right)}^{th}}term+{{\left( \dfrac{n}{2}+1 \right)}^{th}}term \right]$ in which n is the total number of numbers, or terms often called frequency. And in our question they are 10 i.e.$n=10$so put it in the median formula to find it out, so we will get median;
$\begin{align}
  & \dfrac{1}{2}\left[ {{\left( \dfrac{n}{2} \right)}^{th}}term+{{\left( \dfrac{n}{2}+1 \right)}^{th}}term \right] \\
 & = \dfrac{1}{2}\left[ \left( \dfrac{10}{2} \right)^{th}term+\left( \dfrac{10}{2}+1 \right)^{th}term \right] \\
 & = \dfrac{1}{2}\left[ 5^{th} term+6^{th} term \right] \\
\end{align}$
The 5th term and 6^th term are ‘2’ and ‘3’ respectively. As they are the respective terms in the sequence when arranged in ascending order. So put it in above result, which will give us;
$\begin{align}
  &= \dfrac{1}{2}\left[ 2+3 \right] \\
 & =\dfrac{1}{2}\left[ 5 \right] \\
 &= 2.5 \\
\end{align}$
So the median is 2.5.
Hence mean and median are 2.4 and 2.5 respectively.

Note: The formula of median$=\dfrac{1}{2}\left[ {{\left( \dfrac{n}{2} \right)}^{th}}term+{{\left( \dfrac{n}{2}+1 \right)}^{th}}term \right]$is valid only when the total number of numbers/arrangements is even, which is in our case (10 is even number). For an odd number of arrangements median$=\left[ {{\left( \dfrac{n+1}{2} \right)}^{th}}term \right]$ .