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The one-year return (in %) for 24 mutual funds is as follows:

-11.0, -1.7, 0.6, 5.8, -16.2, -7.8, 21.2, -9.9, 4.2, 15.2, -11.9, 4.4, -8.7, 19.2, 21.6, 28.9, 7.4, 2.0, 24.5, -0.7, 7.5, 9.2, -6.7, -10.0

a. Construct a frequency distribution using classes of -20 up to -10, -10 up to 0, etc.

-20 up to -10: 3
-10 up to 0: 7
0 up to 10: 8
10 up to 20: 2
20 up to 30: 4

Total = 24

b. Construct the relative frequency, cumulative frequency, and cumulative relative frequency distributions. (Round "relative frequency" and "cumulative relative frequency" answers to 3 decimal places.)

| Class | Rel. Freq | Cum. Freq | Cum. Rel. Freq |
|--------------|-----------|-----------|----------------|
| -20 up to -10| 0.125 | 3 | 0.125 |
| -10 up to 0 | 0.292 | 10 | 0.417 |
| 0 up to 10 | 0.333 | 18 | 0.750 |
| 10 up to 20 | 0.083 | 20 | 0.833 |
| 20 up to 30 | 0.167 | 24 | 1.000 |

Total Rel. Freq = 1.000

c-1. How many of the funds had returns of at least 20% but less than 30%?

Four funds had returns of at least 20% but less than 30%.

c-2. How many of the funds had returns of 0% or more?

There were 14 funds with returns of 0% or more.

d-1. What percent of the funds had returns of at least -10% but less than 0%? (Round your answer to 1 decimal place.)

29.2% of the funds had a return of at least -10% but not greater than 0%.

d-2. What percent of the funds had returns less than -10%? (Round your answer to 1 decimal place.)

12.5% of the funds had returns less than -10%.

Answer :

Final answer:

Relative frequency is calculated by dividing the frequency of a class by the total number of data points. Cumulative frequency and cumulative relative frequency provide an aggregated count up to a certain data point and its respective proportion.

Explanation:

The concept of relative frequency helps in understanding how often certain results occur in comparison to the total number of outcomes. In a dataset, the relative frequency of each class is calculated by dividing the frequency of that class by the total number of data points. To illustrate this concept, consider a situation where a class has a frequency of 3 out of a total of 100 data points. The relative frequency would then be 3/100 or 0.03. Cumulative frequency and cumulative relative frequency are other important concepts which describe the aggregate frequency up to a certain point in the dataset and the corresponding proportion.

For example, if you have a cumulative relative frequency of 0.28 and a dataset of 50 values, it implies that 28% of the data are below the threshold. This percentage indicates that 14 values (since 28% of 50 is 14) are less than the value at the 28th percentile. If the data values include multiple occurrences of numbers like 4, 5, and 6, and the 14th value is a 6, then the 28th percentile lies between the last six and the first seven, giving us a 28th percentile of 6.5.

Learn more about Relative Frequency here:

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