Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
3. Describing Data Numerically
Mean
Problem 6.5.3a
Textbook Question
Body Temperatures Listed below are body temperatures (°F) of adult males (based on Data Set 5 “Body Temperatures” in Appendix B).
97.6 98.2 99.6 98.7 99.4 98.2 98.0 98.6 98.6
a. Find the mean. Does the result seem reasonable?

1
Step 1: Recall the formula for the mean, which is the sum of all data values divided by the number of data values. Mathematically, it is expressed as: , where is the sum of all data values and is the number of data values.
Step 2: Add up all the body temperature values provided in the dataset: 97.6, 98.2, 99.6, 98.7, 99.4, 98.2, 98.0, 98.6, and 98.6. This will give you the total sum of the data values.
Step 3: Count the number of data values in the dataset. In this case, there are 9 body temperature values.
Step 4: Divide the total sum of the data values (calculated in Step 2) by the number of data values (calculated in Step 3). This will give you the mean body temperature.
Step 5: Interpret the result. Compare the calculated mean to the typical average body temperature of 98.6°F to determine if the result seems reasonable.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Mean
The mean, or average, is a measure of central tendency calculated by summing all values in a dataset and dividing by the number of values. It provides a single value that represents the overall distribution of the data. In this case, to find the mean of body temperatures, you would add all the temperatures together and divide by the total number of temperatures listed.
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Reasonableness of Results
Evaluating the reasonableness of statistical results involves assessing whether the calculated mean accurately reflects the data's characteristics. This can include checking if the mean falls within the range of the data and considering the context of the data, such as typical body temperature ranges for adults. A reasonable result should align with expectations based on prior knowledge.
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Data Set
A data set is a collection of related values or observations, often organized in a structured format. In this question, the body temperatures of adult males form a data set that can be analyzed statistically. Understanding the composition and context of the data set is crucial for accurate calculations and interpretations, such as determining the mean.
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