Question

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

Answer 1

Hint: First of all this is a very simple and a very easy problem. This problem deals with the concepts in statistics. Median and mode are both statistical values in statistics and probability theory. Median is the middle value of the observations when the given set of data or the observations are arranged in the order from lowest to the highest. Mode is the value that appears most of the time in the data.

Complete step-by-step answer:
To find the median arrange the data in the order of lowest to highest, that is arranging the given set of observations in the increasing order, as given below:
The given set of observations is: $12,5,9,6,14,9$ and $8$.
Arranging them in increasing order, as given below:
$ \Rightarrow 5,6,8,9,9,12,14$
Here there are in total 7 observations.
The median is the middle value in the 7 observations.
Here the 4th observation is the middle observation in the 7 observations.
Here the 4th observation is 9.
Hence the median of the given observations is 9.
Now finding the mode out of the 7 observations, for that we have to count each observation, in order to check how many times it has occurred.
Here only 9 occurred twice, whereas all the other observations occurred only once.
As 9 occurred twice, which is maximum out of all the observations.
Hence the mode of the observations is 9.

Median is 9, mode is also 9.

Note:
While finding the median of any given data it is always important to observe the total number of observations correctly, else everything could go wrong. As already discussed, if the total number of observations are odd, then the mean is the middle value of the observation else the median would be the average of the two middle values in the data. While mode would be the mostly recurring element.