MATH 137
Unit 2 & 3: How to Write A Summary Analysis of a Distribution
This is a samplestructure for your summary that describes the distribution of a quantitative variable.
- Begin with a statement that describes the data set.
Example: “The data set consists of the reported ages of 285 students who are enrolled in Math 137 during Fall 2015.”
- Discuss the shape of the distribution. Consider whether the outlier is valid, possibly skewing the graph to the left or right, or if the data point is invalid (for example, if a person’s age in years is 1985, the student probably misread the question, and the value would be excluded). Please discuss both situations.
Example: “Excluding the invalid data point of 1985 years from the distribution, the graph will be symmetric.” “Assuming thatthe outlier is a valid data point, the graph will be skewed to the right.”
- Discuss the center of the distribution. You may use one representative value or a small range of values.
Example: “The center of the distribution is 25 years” or “The center of the distribution is between 24 and 25 years.”
- Discuss the spread of the distribution. Address the overall range and the range of typical values.
Example: “The minimum age is 15 years and maximum age is 70 years, resulting in an overall range of 55 years. The range of typical values is between 19 and 27 years.
- Discuss the outlier(s) of the distribution.
Example: “The data contains one outlier of 1985 years.”
- Write a conclusion or answer the question, if there is one.
Example: “Based on the above information, most of the students (85%) enrolled in Math 137 during Fall 2015appear to be between the ages of 22 and 26 years old.
As you gain more experience in writing paragraphs and calculating percentages, consider incorporating more calculations (focusing your attention on specific bins of the histogram) to strengthen your discussion.
IMPORTANT:
Do not write statements that overgeneralize and draw conclusions for a population instead of the sample (the data you analyzed).
Assignment due next class meeting:
A researcher is interested in comparing the life expectancy of males and females in the United States. The following box plots and sample statistics describe the life expectancy of the two genders. The data was collected in 1999-2001 by state. Write a short essay analyzing and comparing the two data sets. Include the shapes, any outliers and the best measures of center and spread. Make sure to interpret the center and spread in the context of this problem and quote the actual statistics. Include in your conclusion how this information might be useful in the real world and who would be interested in this information?