Question

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

Answer 1

Hint: Arrange the data in ascending or descending order. Median will be the data occurring in the middle. And mode will be the data with the highest frequency.

Complete step-by-step answer:
The data given in the question is:
13, 16, 12, 14, 19, 12, 14, 13, 14.

If we arrange it in ascending order, we’ll get the data as:
12, 12, 13, 13, 14, 14, 14, 16, 19.

Total number of observations in the data $ = 9$
And we know that mode of the data is the observation with highest frequency i.e. the observation which is occurring maximum number of times.

As we can see from the data that 14 is occurring three times which is maximum.
Therefore, mode of the data $ = 14$

Median of the data is the observation occurring in the middle when data is arranged in either ascending or descending order. So, if we look at the data arranged in ascending order above, the middle observation is 14.

Thus, the median of the data $ = 14$.

Note: For finding the median of the data, we always have to arrange it in order, either ascending or descending order. Further, if we have to calculate the mean of the data, we can do so by applying the formula:
Mean $ = \dfrac{{{\text{Sum of observations}}}}{{{\text{number of observations}}}}$.