Let's break down the problem and organize the given data into a frequency table.

Step 1: Analyze the Data

1. Total Units: 500 units.
2. Return Range: 0% to 30%.
3. Frequency Distribution:
   • 5% of units (0% to 5%): $5\% \times 500 = 25$ units.
   • 15% of units (5% to 10%): $15\% \times 500 = 75$ units.
   • The median rate of return is 15%.
   • The upper quartile is 20%.
   • 50 units earned returns between 25% and 30%.

Step 2: Construct the Frequency Table

Given the above data, we can construct the frequency table as follows:

Return Range (%)	Number of Units	Cumulative Frequency
0 - 5	25	25
5 - 10	75	100
10 - 15	$x_1$	$100 + x_1$
15 - 20	$x_2$	$100 + x_1 + x_2$
20 - 25	$x_3$	$100 + x_1 + x_2 + x_3$
25 - 30	50	500

Step 3: Solve for the Unknowns

We know that the median return is 15%, meaning that half of the units (250) earned less than or equal to 15%. Therefore, the cumulative frequency at the 15% mark should be 250 units.

So, $100 + x_1 = 250$ implies: $x_1 = 250 - 100 = 150 \text{ units in the range } 10\%-15\%.$

The upper quartile is at 20%, meaning that 75% of the units (375 units) earned less than or equal to 20%.

So, $100 + 150 + x_2 = 375$ implies: $x_2 = 375 - 250 = 125 \text{ units in the range } 15\%-20\%.$

Finally, there are 50 units in the range 25%-30%, so: $x_3 = 500 - (100 + 150 + 125 + 50) = 75 \text{ units in the range } 20\%-25\%.$

Final Frequency Table

Return Range (%)	Number of Units	Cumulative Frequency
0 - 5	25	25
5 - 10	75	100
10 - 15	150	250
15 - 20	125	375
20 - 25	75	450
25 - 30	50	500

Step 4: Identify Maximum Concentration

The range with the maximum number of units (maximum concentration) is 10% to 15% with 150 units.

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Do you want more details or have any questions?

Here are five related questions:

1. How would the frequency table change if 10% of units had returns from 0% to 5%?
2. What is the interquartile range for the return on investment?
3. How would you calculate the mode of this dataset?
4. What would be the impact if the number of units in the 25%-30% range doubled?
5. How does the cumulative frequency help in understanding the distribution?

Tip: When analyzing distributions, the cumulative frequency helps in understanding the spread and concentration of data, especially around key statistical points like the median and quartiles.