Final answer:
To determine the values of x and y in the frequency distribution where the median is 28.5, we use the cumulative frequency approach. By analyzing the distribution, we find that x equals 5 and y equals 10.
Step-by-step explanation:
To find the values of x and y in the given frequency distribution with a known median, first arrange the data in ascending order. Since there are 60 data points in total, the median would be the average of the 30th and 31st values. The frequency just before the median value is cumulative; adding the frequencies will give us the position of these values.
The frequency for the class interval 20-30 is given as 20, so the cumulative frequency up to this point is 5 (0-10) + x (10-20) + 20 (20-30). If 28.5, which is the median, falls in the class interval 30-40, the cumulative frequency just before this interval must be less than or equal to 30 and at least 29 (since the median is not less than 28.5 but less than 30). Hence, 5 + x + 20 should be less than or equal to 30, which tells us that x must be 5.
Now, because the median class interval does not include the upper limit (40), this means 5 (0-10) + 5 (10-20) + 20 (20-30) + some amount from 15 (30-40) totals to 30. So we have 30 values before reaching 40. As a result, the cumulative frequency up to class interval 40-50 must be less than 45 because we know there are 15 values in interval 30-40, and we have accounted for 30 values until the 40 mark. We now solve for y in the 40-50 interval knowing that the total frequency is 60: 5 + 5 + 20 + 15 + y + 5 = 60, which simplifies to y = 10.
Therefore, x equals 5 and y equals 10 in the given frequency distribution where the median is 28.5.