Question

Find the mode and median of the data: $13,16,12,14,19,12,14,13,14$

Answer 1

Step 1: Find the mode of the data

Mode is the value in the data that occurs most frequently.

Given data, $13,16,12,14,19,12,14,13,14$

Arrange this in ascending order, we get $12,12,13,13,14,14,14,16,19$

Upon observation, we can see that $14$ occurs three times making it the most repeated variable.

So,$\mathrm{mode}=14$.

Step 2: Find the median of the data

Median is the middle most value of the data.

The given data arranged in ascending order is $12,12,13,13,14,14,14,16,19$

There are $9$ observations (n) in total and we know that for an odd number of observations, $\mathrm{median}=\mathrm{value}\mathrm{of}{\left(\frac{\mathrm{n}+1}{2}\right)}^{\mathrm{th}}\mathrm{term}$

So, the median term will be,

$$\begin{gathered} ={\left(\frac{9+1}{2}\right)}^{\mathrm{th}}\mathrm{term} \\ =5^{\mathrm{th}}\mathrm{term} \end{gathered}$$

So, the $5^{th}$ term of the data is$14$.

Hence, both the median and mode of the given data is$14$.