CAT 2024 Slot 2 — DILR Question 12

Mixed PracticeEasy

Passage / Data

Answer the following questions based on the information given below.

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.

Distribution of ratings on Day 2

Rating (Day 2)	1	2	3	4	5
Number of buyers	5	10	5	20	10

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.

What is the median of all ratings given on Day 3?

Answer & solution

Correct answer: 4

Answer: 4

Solution

Medium

With 100 ratings, the median is the average of the 50th and 51st values. Use the Day-3 counts (10, 10, 20, 30, 30) to locate them.

Day 3 counts: rating 1→10, 2→10, 3→20, 4→30, 5→30 (cumulative 10, 20, 40, 70, 100).

Locate the middle positions. Cumulative counts: ratings 1–3 fill positions 1–40; rating 4 fills 41–70.

\begin{aligned} &\text{50th, 51st positions} \in [41,70]\\ &\Rightarrow\ \text{both have rating }4 \end{aligned}

Median.

\begin{aligned} &\frac{4+4}{2}=4 \end{aligned}

4

CAT 2024 Slot 2 — DILR Question 12

Answer & solution

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