Question

Find the median of the following data:
$3,1,5,6,3,4,5,6$.

Answer 1

Hint: Here, we will first arrange the given data in ascending or descending order and then, we will count the number of observations. After finding whether the number of observations are odd or even, we will apply the median formula accordingly. Using the formula, we will be able to find the required median of the given data.

Formula Used:
Median of even observations $ = {\dfrac{n}{2}^{th}}$ observation, where $n$ represents the number of observations in the data.

Complete step-by-step answer:
The given data is $3,1,5,6,3,4,5,6$
Now, in order to find the median of the given data, first of all, we will arrange this data in ascending order.
This means that we will arrange this data from the smallest to the largest number.
Hence, after arranging in ascending order, we get,
$1,3,3,4,5,5,6,6$
Now, if we count the number of terms in the data, then, we can observe that there are 8 terms in this data.
Hence, we are required to find the median of 8 observations.
Now, 8 is an even number because it is divisible by 2 and can be written in the form of $2a$ where, $a$ is the constant required to be multiplied by 2 to get the number 8.
Hence, we will use the formula of the median of even observations as: ${\dfrac{n}{2}^{th}}$ observation.
Hence, substituting $n = 8$, we get,
The median of the given data $ = {\dfrac{8}{2}^{th}} = {4^{th}}$ observation
Hence, the ${4^{th}}$ observation in the data where the observations are arranged in the ascending order is: 4

Therefore, the median of the given data is 4.
Hence, this is the required answer.

Note:
The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average. While the average and median can be the same or nearly the same, they are different if more of the data values are clustered towards one end of their range and this is called skewness.