GF582 Unit 2 Bond Fund Descriptive Statistics Example

Course	GF582 Statistical Methods for Decision Making
Unit	Unit 2
Paper type	Descriptive statistics write-up
Length	About 970 words, 6 pages double-spaced
Format	APA 7 student paper
School	Purdue University Global
Program	MS in Finance
Updated	October 2026

Free sample paper for GF582 Unit 2

Two Numbers Hide the Bad Months: A Unit 2 Descriptive Statistics Write-Up on a High-Yield Bond Fund

[Student Name]

Purdue University Global

GF582: Statistical Methods for Decision Making

Unit 2 Descriptive Statistics Write-Up

[Instructor Name]

[Date]

The fund and its 120 monthly returns are composite and illustrative; the articles and textbook cited are real.

What this part is doingStating the dataset and the shortcoming of the usual summary in the lead tells the grader what the write-up will add.

The Data and the Question

The dataset holds ten years of monthly total returns, net of fees, for a high-yield bond fund offered to employees of a regional hospital system. The fund's fact sheet reports an average monthly return of 0.48 percent and a standard deviation of 1.72 percent. The plan's committee wants to know whether those two numbers give participants a fair picture of what holding the fund feels like.

The Summary Table

1. Mean monthly return: 0.48 percent.

2. Median monthly return: 0.76 percent.

3. Standard deviation: 1.72 percent.

4. Skewness: negative 1.23.

5. Excess kurtosis: 3.41.

6. First quartile: negative 0.39 percent. Third quartile: 1.59 percent.

7. 5th percentile: negative 2.08 percent.

8. Worst month: negative 7.28 percent.

9. Negative months: 40 of 120.

10. Largest peak-to-trough decline: about 14.6 percent, over seven months.

Reading the Center

The median, 0.76 percent, sits well above the mean, 0.48 percent. In a symmetric distribution they would be close. A median above the mean signals a distribution pulled down by a few large losses: most months are moderately good, and a handful of bad months drag the average down. A participant asked what a typical month looks like should hear the median; a participant asked what the fund earned on average should hear the mean.

Reading the Spread

The interquartile range, from negative 0.39 to 1.59 percent, contains the middle half of months and is about 1.98 points wide. If returns were normal, that range would be about 1.35 standard deviations wide, about 2.32 points. The narrower actual range shows that ordinary months cluster more tightly than a normal distribution would predict, while the tails stretch further.

Reading the Tails

Skewness of negative 1.23 confirms the long left tail. Excess kurtosis of 3.41 means extreme months, in either direction but here mostly losses, occur far more often than a normal distribution allows.

The worst month, negative 7.28 percent, is about 4.5 standard deviations below the mean. Under a normal distribution, a month that bad would be expected roughly once in tens of thousands of years. It happened once in ten. Ratios built on the mean and standard deviation, such as the Sharpe ratio (Sharpe, 1966), inherit the same blind spot, since they treat a large loss and a large gain as equally likely.

The fact sheet's mean and standard deviation describe a fund whose bad months are mild and rare, but the data show losses that are rarer than average months and much larger when they come, which is exactly the risk a participant feels and the two numbers hide.

What this part is doingThe highlighted sentence explains why the standard summary misleads for this fund, the judgment graders look for in a descriptive write-up.

The Histogram

A histogram with half-point bins shows a tall cluster of months between 0 and 2 percent, a gentle slope to the right that ends near 4 percent, and a long, thin tail to the left with isolated months below negative 3 percent, including the negative 7.28. Overlaying a normal curve with the same mean and standard deviation shows the curve too low in the center and far too thin in the left tail.

The Drawdown Chart

The fund's largest decline from a peak, about 14.6 percent, unfolded over seven months during a period of widening credit spreads and took about fourteen months to recover. Drawdown captures something the monthly figures cannot: losses that accumulate. A participant who looked at the statement after month seven would have seen a balance down by about a seventh.

Why High-Yield Returns Look Like This

High-yield bonds pay steady coupons most months, producing the cluster of moderate gains. When the economy weakens, defaults rise and bond prices fall together, producing the occasional sharp loss. Research on fund returns has documented that many asset classes show negative skewness and fat tails, and that measures built only on mean and variance misjudge their risk (Harvey & Siddique, 2000). Textbook treatments of descriptive statistics recommend reporting quartiles, percentiles and the extreme observation alongside the standard deviation whenever a distribution is skewed (Anderson et al., 2020).

How the Fund Compares With a Normal Benchmark

A useful exercise is to ask what a normal distribution with the same mean and standard deviation would have predicted. It would expect about 6 of 120 months below negative 2.35 percent, the normal 5th percentile; the fund had 6 months below negative 2.08, so the frequency of moderately bad months is close to normal. The difference lies further out. A normal distribution would expect essentially no month below negative 5 percent; the fund had three. It is the size of the worst months, not their number, that the standard summary misses.

What a Participant Experiences

For a participant with $40,000 in the fund, the mean month adds about $190 and the median month about $300. The 5th percentile month subtracts about $830, and the worst month subtracted about $2,900. The fourteen-month recovery from the largest decline meant that a participant who checked statements quarterly saw four quarters in a row below the earlier peak. These are the figures that shape whether people stay invested, and they are absent from the fact sheet.

Recommendation for the Committee

Add three figures to the participant fact sheet: the median month, the 5th percentile month and the largest decline from a peak. Together with the mean and standard deviation, they give participants a picture of both the typical experience and the bad stretches.

Conventions

Skewness and kurtosis are sample statistics; excess kurtosis subtracts 3 so that a normal distribution scores zero. Percentiles use linear interpolation between ranked observations.

What this part is doingEnding on conventions shows how each statistic was computed so a grader can reproduce it.

References

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2020). Statistics for business and economics (14th ed.). Cengage.

Harvey, C. R., & Siddique, A. (2000). Conditional skewness in asset pricing tests. The Journal of Finance, 55(3), 1263-1295. https://doi.org/10.1111/0022-1082.00247

Sharpe, W. F. (1966). Mutual fund performance. The Journal of Business, 39(1), 119-138. https://doi.org/10.1086/294846

The Purdue Global GF582 Unit 2 instructions

Unit 2 of GF582 asks you to summarize a supplied dataset and choose the statistics that describe it honestly. Report measures of center, spread and shape, including the median, quartiles, percentiles, skewness, kurtosis and the extreme values, not only the mean and standard deviation. Interpret each in plain words for the reader the data concern. Compare the actual distribution with a normal distribution of the same mean and spread, using a histogram and, for returns, a drawdown measure. Explain why the data take the shape they do. Translate the statistics into what a participant or decision maker would actually experience. Recommend which figures should be reported. State how each statistic was computed. Cite a statistics text and research on the distribution's features in APA 7.

How this GF582 Unit 2 example is built

A section on the dataset and the committee's question opens the sample, followed by a ten-line summary table. Separate sections read the center, the spread and the tails, and the highlighted sentence explains why two numbers hide the bad months. The tails section compares the worst month with what a normal distribution would predict and notes, citing Sharpe, that ratios built on mean and variance share the blind spot. Sections on the histogram and the drawdown follow. A section explains high-yield return patterns with Harvey and Siddique on skewness and Anderson and colleagues on reporting skewed data. A comparison with a normal benchmark and a translation into dollars for a $40,000 participant precede the recommendation to add three figures to the fact sheet.

Reading the GF582 Unit 2 grading rubric

GF582 graders reward a summary chosen to fit the data. Correct computation and clear labeling of each statistic earn the first share of points. The next share goes to interpretation in plain language: what a median above the mean means, what negative skewness and high kurtosis imply, and how the worst month compares with normal expectations. Visual displays earn credit when they are used to make a point. Instructors in the MS in Finance program value translating statistics into the reader's experience, such as dollars on a typical balance. A practical recommendation, stated computation methods and APA 7 references to a text and a study of return shapes complete the grade.

GF582 Unit 2 help: mistakes that cost points

The most common GF582 Unit 2 error is reporting only the mean and standard deviation for data that are clearly skewed. Others list skewness and kurtosis values without saying what they mean. Percentiles are computed but never compared with what a normal distribution would predict. Histograms use bins so wide that the tail disappears. Drawdowns are omitted for return data, though they capture losses that accumulate. Recommendations are missing, so the write-up ends as a table. For any dataset your course supplies, keep the steps: center, spread, shape, extremes, a normal comparison, a reader's view and a reporting recommendation.

Get a GF582 Unit 2 example written to your instructions

The dataset supplied with Unit 2, the software your section uses and the rubric are all it takes. A custom write-up picks the summary that dataset's shape supports and explains each choice, and it arrives within 24-48h; the first request is free. If the prompt names an audience, the explanations are pitched to that reader. The paper above is an original model document written by our desk, not a submitted student paper and not an official Purdue University Global document.

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GF582 Unit 2 questions, answered

Which measure of center should a skewed dataset report?

Usually both mean and median, with a sentence on why they differ. The median describes a typical observation; the mean matters when outcomes add up, as returns do over time. For returns, the geometric mean describes actual compounded growth and is worth adding. Reporting one measure alone hides the shape the assignment is often designed to reveal.

Do skewness and kurtosis need to be interpreted?

Yes, in plain words. Negative skewness means large losses are more common than gains of the same size; high kurtosis means more extreme months than a normal curve predicts. Each figure should be followed by what it implies for the decision at hand, such as whether a standard deviation understates the risk a reader cares about.

How many bins should the histogram have?

Enough to show the shape without turning noise into bars. For about a hundred observations, ten to fifteen equal-width bins is a common starting point, adjusted so that bin edges fall on readable values. State the width, label both axes, and check that the tail is visible, since a tail hidden in one wide bin defeats the purpose.

Where can I find a free GF582 Unit 2 sample paper?

You can read a full GF582 Unit 2 descriptive statistics write-up on a high-yield bond fund's 120 monthly returns here, with skewness, kurtosis, percentiles, a drawdown and APA 7 references.

Why is the median return above the mean?

Most months are moderately positive, but a few large losses pull the average down. A median above the mean is the signature of a distribution with a long left tail.