Question

Find the marks of 15 students in an examination are: 25, 19, 17, 24, 23, 29, 31, 40, 19, 20, 22, 26, 17, 35, 21. Find the median score.

Answer 1

Hint: First we will use formula to calculate median value by first calculating \[\dfrac{{n + 1}}{2}\], where \[n\] is the number of values in a set of data and then find the value of median by taking the value directly.

Complete step-by-step answer:
We are given that the observations are 25, 19, 17, 24, 23, 29, 31, 40, 19, 20, 22, 26, 17, 35, 21.
First, we will arrange the given numbers in ascending order, we get
17, 17, 19, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 35, 40
We know the formula to find the median value by first calculating \[\dfrac{{n + 1}}{2}\], where \[n\] is the number of values in a set of data.
After finding the number of observations, we have that \[n = 15\].
Substituting the value of \[n\] in the above formula, we get
\[
   \Rightarrow \dfrac{{15 + 1}}{2} \\
   \Rightarrow \dfrac{{16}}{2} \\
   \Rightarrow 8 \\
 \]
 So, we will take the 8th terms from the terms in ascending orders, we have 23.
Therefore, the required value is 23.

Note: We need to know that the mean is adding the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count. Do not forget any marks by adding up the values, so be prepared for that. We need to know if the value from \[\dfrac{{n + 1}}{2}\], where \[n\] is the number of values in a set of data is an integer than there is only one median value or else there will be two values.