Question 16

Explanation

We are asked to find the value of $a$ based on information about the average of Group II and the mode of Group I.

Determining the Mode of Group I

Data for Group I: $3, 5, 5, 8, 9$.

The mode is the value that appears most frequently. From the data, the value $5$ appears 2 times, while other values appear only once.

So, Mode of Group I $= 5$.

Determining the Average of Group II

It is given that the average of Group II is two more than the mode of Group I.

Finding the Value of $a$

The average formula is the sum of all data divided by the number of data points. Data for Group II: $4, 6, 8, 8, a$. There are 5 data points.

Multiply both sides by 5:

Move 26 to the left side:

Thus, the value of $a$ is $9$.