Question

Find the median and mode of the following observation.
$12,5,9,6,14,9$ and $8$.

Answer 1

Arrange the data in ascending or descending order. Median will be the data occurring in the middle. And the mode will be the data with the highest frequency. We will get the required median and mode easily.

Complete step-by-step solution:
It is given the question stated as the number of series $12,5,9,6,14,9$ and $8$.
Here we have to find the median and mode of the given data.
First we are finding the mode of the given data
If we arrange the data in ascending order, we will get the data as: $5,6,8,9,9,12,14$
If we arrange the data in descending order, we will get the data as $14,12,9,9,8,6,5$
We preferably follow the ascending order
Total number of observations is in the data $= 7$
And we know that mode of the data is the observation with the highest frequency that is the observation which is occurring the maximum number of times.
As we can see from the data that $9$ is occurring two times this is maximum.
Therefore the mode of the data is $= 9$
Now we need to find out the median of the given data.
Median of the data is the observation occurring in the middle when the data is arranged in either in the ascending order or in the descending order.
Therefore if we look at the data arranged in ascending order above, the middle most observation is $9$.
Hence the median of the given data is $= 9$

Note: Here we need to know about some series
$1)$ Individual series: With all having frequencies as $1$.
$2)$ Discrete series: In this series also has numbers, but the frequency is not necessarily equal to $1$, it may be more than different from one another.
Let’s have an example for individual series: $22,23,24,25,26,27,28,30,65$ is the individual series because none of them have frequency more than one.
Example for discrete series:
The class $20 - 30$ contains $6$ observations $25,25,20,22,25$ and $28$.
So when these data are grouped as class $20 - 30$ in the frequency distribution, the latter provides only the number of records in that class (frequency $= 6)$ but not their actual values.