Question

A dice is rolled 8 times and the numbers appearing are noted:
6, 4, 2, 1, 2, 5, 2, 1.
Which of the follwing options is true regarding the above set of observations?

• A. Median = 3, Mode =1
• B. Median = 2, Mode =2
• C. Median = 1, Mode =2
• D. Median = 4, Mode = 1

Answer 1

The correct option is B Median = 2, Mode =2

Median is the middlemost observation when all the data points of a dataset are arranged in either ascending or descending order.

Organising the given dataset in ascending order, we have:
1, 1, 2, 2, 2, 4, 5, 6.

Here, the total number of terms is 8, and hence the median will be the average of the two data points in the middle.

i.e., Median = Average of the $4^{\text{th}}$ and $5^{\text{th}}$ observations in the dataset
= $\frac{2+2}{2}=2$

Mode is the most frequently occuring observation in the dataset.
Here, 2 occurs the maximum number of the time(3 times).

Hence, median = 2 and mode = 2 for the given dataset.