Question

The daily wages (in rupees) of 19 workers are 41, 21, 38, 27, 31, 45, 23, 26, 29, 30, 28, 25, 35, 42, 47, 53, 29, 31, 35. Find the median.

Answer 1

Hint:
Here, we need to find the median of the daily wages of 19 workers. The median is defined as the middle value of a series. First we have to arrange the numbers in ascending order and then use the formula to find the median. Then, we will find the obtained term from the series arranged in the ascending order.
Formula Used: We will use the formula Median \[ = {\left( {\dfrac{{n + 1}}{2}} \right)^{th}}\] term when the number of terms \[n\] is odd.

Complete step by step solution:
The median is the \[{\left( {\dfrac{{n + 1}}{2}} \right)^{th}}\] term when the number of terms is odd, or the average of the \[{\left( {\dfrac{n}{2}} \right)^{th}}\] and \[{\left( {\dfrac{{n + 1}}{2}} \right)^{th}}\] when the number of terms is even.
Now, we will arrange the given series in ascending order.
Thus, we get 21, 23, 25, 26, 27, 28, 29, 29, 30, 31, 31, 35, 35, 38, 41, 42, 45, 47, 53.
The number of terms in the series is 19, which is an odd number. Therefore, the median is the \[{\left( {\dfrac{{n + 1}}{2}} \right)^{th}}\] term of the series.
Substituting 19 for \[n\] in the expression, we get
\[\begin{array}{l}{\rm{Median}} = {\left( {\dfrac{{19 + 1}}{2}} \right)^{th}}\\ = {\left( {\dfrac{{20}}{2}} \right)^{th}}\\ = {{10}^{th}}{\rm{ term}}\end{array}\]
The median is the 10th term of the series. The 10th term of the series (in ascending order) is 31. Therefore, the median of the given series is 31.

This means that the median daily wage of the 19 workers is 31 rupees.

Note:
For solving this question, we must know the difference between mean, median and mode. The arithmetic average of a data is called the arithmetic mean of the data. The mode is that number of the data which appears most frequently in that data set. Median is the middle number of the data. The formula of the median is different for even and odd numbers of observations. So, it is important for us to remember both the formulas.
Second thing we need to keep in mind is that whenever we find the median, we should check if the given series is in ascending order or not. It is a common mistake to use the given series without arranging it in ascending order to find the median. For example, the 10th term of the given series is 30, which is wrong.