Question

The median of the data
49, 48, 15, 20, 28, 17, 14 and 10 is

Answer 1

Hint: To find the median, it is first of all necessary to arrange the data in ascending order.
Then we have to determine the number of values in the given data set. If the number of values are odd then the middle value will be the median. If the number of values is even then we will have to take the average of the middle two values as the median for the given data set.

Complete step-by-step answer:
Median is the middle value of the set of data when the data is arranged in an ascending order. The median of a data has a higher frequency if the data is distributed symmetrically.
We will arrange the given data in ascending order as 10, 15, 14, 17, 20, 28, 48 and 49.
Also, the number of values here is 8, which is an even number. As we know if the number of values is even in the data, then the average of the two middle values will be the median. For 8 numbers, the middle values will be the \[{4^{th}}\] and \[{5^{th}}\] numbers from either side.
In the given data, as we can see that the \[{4^{th}}\] and \[{5^{th}}\] values are 17 and 20.
So, the median will be the average of these two values which will be given as \[\Rightarrow \dfrac{{17 + 20}}{2} = \dfrac{{37}}{2} = 18.5\].
Thus, the median of the data will be 18.5.

Note: To find median, it is important to first of all arrange the given numbers in ascending order. Median does not indicate the average of the data set, however it is more or less close to the mean of the data, this is because if the frequency of a particular number is higher than the median will be closer to that number, thus closer to the mean.