PSY 315 Week 1 Descriptive Statistics and Graphs Example

Sleep, Caffeine and Exam Scores: Describing a Class Survey With Descriptive Statistics and Graphs

[Student Name]

University of Phoenix

PSY/315: Statistical Reasoning in Psychology

Week 1 Assignment

[Instructor Name]

[Date]

The survey, the students and all numbers are composites written for a model paper; statistical guidance comes from the sources listed.

Statistics begins with description, which Gravetter and Wallnau (2017) treat as the first step in any analysis. Before testing any idea, a researcher needs to know what the data look like: their typical values, how spread out they are and their shape. This report describes a composite class survey to show how descriptive statistics and graphs are chosen and interpreted.

The Data

A psychology instructor at a community college in Phoenix, Arizona, asked 120 students in three sections to complete a short anonymous survey. Students reported how many hours they slept on a typical school night, how many cups of caffeinated drinks they had each day, their stress level on a scale from 1, very low, to 10, very high, and their score on the most recent course exam, out of 100. The question behind the survey was whether sleep and caffeine relate to stress and exam performance, but this report describes the variables before any relationships are tested.

Scales of Measurement

Each variable has a scale that determines which statistics fit. Sleep hours and cups of caffeine are ratio variables: they have equal intervals and a true zero. Exam scores are treated as interval or ratio, since points are equal in size. The stress rating is ordinal: a rating of 8 is higher than 4, but the distance between ratings may not be equal across the scale. Knowing the scale prevents errors such as averaging categories that have no numeric meaning.

Sleep Hours

Sleep ranged from 4 to 9 hours. The mean was 6.4 hours and the median 6.5, close together, which suggests a roughly symmetric distribution. The standard deviation was 1.1 hours, meaning most students slept within about an hour of the average. A histogram shows a single peak around six to seven hours and tails on both sides.

Caffeine

Caffeine is different. Most students reported one or two cups, and twenty reported none, but eight students reported six or more cups, with one reporting ten. The mean was 2.1 cups and the median 1.5 cups. Because the few heavy drinkers pull the mean upward, the median better describes a typical student. The distribution is positively skewed, with a long tail to the right.

Micceri (1989) inspected 440 large distributions of achievement and psychometric scores and reported that hardly any were truly normal; most were skewed, lumpy or had heavy tails. Caffeine data like these are a common example, and they show why researchers should look at a distribution before choosing statistics.

Stress Ratings

Because stress ratings are ordinal, the median and the frequency of each rating describe them best. The median was 6, and the most frequent rating, the mode, was 7. A frequency table shows that 45 students, about 38 percent, rated their stress 7 or higher. A bar chart, with each rating as a separate bar, displays this clearly.

Exam Scores

Exam scores ranged from 48 to 98, with a mean of 76.3, a median of 77 and a standard deviation of 11.2. The histogram is roughly bell-shaped with a slight tail toward lower scores. About two-thirds of students scored between 65 and 88, roughly within one standard deviation of the mean, which is what a near-normal distribution would predict.

The average student drank 2.1 cups of caffeine, but no typical student drank that much; the mean was pulled up by a few very heavy drinkers.

Choosing Graphs

Cumming and Finch (2005) argued that well-designed graphs, especially those showing confidence intervals, help readers understand data and the uncertainty around estimates, and they offered rules for interpreting such pictures correctly. For description, the principle is to choose graphs that show the shape of the data honestly. Histograms suit sleep, caffeine and exam scores because they reveal shape and outliers. A box plot of caffeine highlights the skew and the extreme values. A bar chart suits the stress ratings. Pie charts would hide most of this information.

Building the Frequency Table

A grouped frequency table for exam scores uses intervals of ten points, from 40 to 49 up to 90 to 99. Three students fell in the lowest interval, 31 in the 70 to 79 interval, the largest group, and 14 in the top interval. Adding a cumulative percentage column shows that 29 percent of students scored below 70, the passing line in many courses. A table like this lets an instructor see at a glance where most students land and how many need extra help before the next exam.

Checking for Outliers

The student who reported ten cups of caffeine was checked against the original survey form to rule out a typing error. The answer was written clearly, so the value was kept. Removing real data because it is inconvenient would bias the description; reporting the median alongside the mean handles the problem honestly.

Variability Beyond the Standard Deviation

The range is easy to compute but sensitive to one extreme value; the single student who drank ten cups stretches the caffeine range to ten. The interquartile range, which covers only the central 50 percent of cases, is more stable. For caffeine, the middle half of students drank between one and three cups, a range that describes most students better than the full range.

What the Description Suggests

The description already raises questions for later weeks. Many students sleep less than seven hours, more than a third report high stress and caffeine use varies widely. Whether sleep or caffeine relate to stress or exam scores requires inferential statistics, covered in later weeks. Description also shows that caffeine's skew may call for rank-based methods or a transformation when testing relationships.

Reporting in APA Style

In APA style, descriptive statistics are reported with symbols in italics, such as M = 6.40 hours, SD = 1.10, for sleep, and Mdn = 1.50 cups for caffeine. Tables should have numbers and titles, and figures should have labeled axes and captions explaining what is shown.

Conclusion

Describing the survey shows that each variable needs its own approach: means and standard deviations for symmetric sleep and exam scores, medians and interquartile ranges for skewed caffeine and medians and frequencies for ordinal stress ratings. Graphs chosen to show shape honestly make these patterns visible and prepare the data for the tests to come.

References

Cumming, G., & Finch, S. (2005). Inference by eye: Confidence intervals and how to read pictures of data. American Psychologist, 60(2), 170-180. https://doi.org/10.1037/0003-066X.60.2.170

Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for the behavioral sciences (10th ed.). Cengage Learning.

Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105(1), 156-166. https://doi.org/10.1037/0033-2909.105.1.156