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The Practice of Statistics, 5th Edition
Starnes, Tabor, Yates,& Moore
Chapter 2: Modeling Distributions of Data
Key Vocabulary:
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percentile
cumulative relative
frequency graph
ogive
standardized value
z-scores
linear transformations
density curve
2.1
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normal distribution
normal curve
inflection point
68-95-99.7 (Empirical)
rule
standard normal
distribution
standard Normal Table
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N  , 
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normal probability plot
Describing Location in a Distribution (pp. 85 – 98)
1. What is a percentile?
2. Is there a difference between the 80th percentile and the top 80%? Explain.
3. Is there a difference between the 80th percentile and the lower 80%? Explain.
4. What type of graph is used to display percentiles?
5. Which percentiles are used in a 5-Number Summary?
6. What is the purpose of standardizing a variable?
7. Explain how to standardize a variable.
Chapter 2: Density Curves and Normal Distribution
The Practice of Statistics, 5th Edition
Starnes, Tabor, Yates,& Moore
8. What is a z-score?
9. When you add a constant, a, to each value in a data set, which statistical measures change?
Which stay the same?
10. When you multiply all the values in a data set by a constant, b, which statistical measures change?
11. What effect would standardizing every observation in distribution have on the:
Shape:
Center:
Spread:
Resulting set of z-scores:
2.2
Density Curves and Normal Distributions (pp. 103 – 127)
1. What are the 4 steps (Toolbox) you should follow when exploring quantitative data from a single
variable?
2. What is a density curve?
Chapter 2: Density Curves and Normal Distribution
The Practice of Statistics, 5th Edition
Starnes, Tabor, Yates,& Moore
3. What does the area under a density curve represent?
4. Where is the median of a density curve located?
5. Where is the mean of a density curve located?
6. How does the skewness of a density curve affect the relationship between the mean and the median?
7. How would you describe the shape of a Normal curve? Draw several examples.
8. Where on the Normal curve are inflection points located?
9. Where is the mean of a Normal curve?
10. How do you abbreviate the Normal distribution with mean, μ and standard deviation, σ?
Chapter 2: Density Curves and Normal Distribution
The Practice of Statistics, 5th Edition
Starnes, Tabor, Yates,& Moore
11. Explain the Empirical or 68-95-99.7 Rule.
12. What is the standard Normal distribution?
13. What information does the standard Normal table give?
14. How do you use the standard normal table (Table A) to find the area under the standard normal curve
to the left of a given z-value? Draw a sketch.
15. How do you use Table A to find the area under the standard normal curve to the right of a given zvalue? Draw a sketch.
16. How do you use Table A to find the area under the standard normal curve between two given zvalues? Draw a sketch.
17. How do you use Table A to find the observed value with a given proportion in the body of the table
above or below it?
Chapter 2: Density Curves and Normal Distribution
The Practice of Statistics, 5th Edition
Starnes, Tabor, Yates,& Moore
18. What are the 3 steps you should ALWAYS follow when solving problems involving Normal
distributions?
Step 1.
Step 2.
Step 3.
19. What are the 3 steps you should ALWAYS follow to find values from areas in any Normal distribution?
Step 1:
Step 2:
Step 3:
20. Describe two methods for assessing whether or not a distribution is approximately normal.
21. How do you use Normal probability plots?
Chapter 2: Density Curves and Normal Distribution