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An online e-commerce firm receives daily integer product ratings from 1 through 5 given by buyers. The daily average is the average of the ratings given on that day. The cumulative average is the average of all ratings given on or before that day. The rating system began on Day 1, and the cumulative averages were 3 and 3.1 at the end of Day 1 and Day 2, respectively. The distribution of ratings on Day 2 is given in the figure below.

The following information is known about ratings on Day 3.

1. 100 buyers gave product ratings on Day 3.

2. The modes of the product ratings were 4 and 5.

3. The numbers of buyers giving each product rating are non-zero multiples of 10.

4. The same number of buyers gave product ratings of 1 and 2, and that number is half the number of buyers who gave a rating of 3.

Question 13.

Which of the following is true about the cumulative average ratings of Day 2 and Day 3?

The cumulative average of Day 3 increased by less than 5% from Day 2.

The cumulative average of Day 3 decreased from Day 2.

The cumulative average of Day 3 increased by a percentage between 5% and 8% from Day 2.

The cumulative average of Day 3 increased by more than 8% from Day 2.

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Text Explanation

The cumulative average rating at the end of day 3 would be $\frac{\left(3.1\times\ 200\right)+\left(3.6\times\ 100\right)}{200+100}$

[the cumulative average rating on day 2= 3.1

Number of ratings received by day 2= 200]

$\frac{360+620}{300}=\frac{980}{300}=3.266$

The increase in the cumulative average from day 2 to day 3 can be calculated as $\frac{3.266-3.1}{3.1}\times\ 100\approx\ 5.34$

Which aligns with the statement given in option C.

Therefore, Option C is the correct answer.

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Question 13.

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