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# One-Variable Data Analysis Rapid Review for AP Statistics

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By — McGraw-Hill Professional
Updated on Feb 5, 2011

Review the following concepts if necessary:

### Rapid Review

1. Describe the shape of the histogram below:
2. .

Answer: Bi-modal, somewhat skewed to the left.

3. For the graph of problem #1, would you expect the mean to be larger than the median or the median to be larger than the mean? Why?
4. Answer: The graph is slightly skewed to the left, so we would expect the mean, which is not resistant, to be pulled slightly in that direction. Hence, we might expect to have the median be larger than the mean.

5. The first quartile (Q1) of a dataset is 12 and the third quartile (Q3) is 18. What is the largest value above Q3 in the dataset that would not be an outlier?
6. Answer: Outliers lie more than 1.5 IQRs below Q1 or above Q3. Q3 + 1.5(IQR) = 18 + 1.5(18 - 12) = 27. Any value greater than 27 would be an outlier. 27 is the largest value that would not be an outlier.

7. A distribution of quiz scores has = 35 and s = 4. Sara got 40. What was her z-score? What information does that give you?

.

This means that Sara's score was 1.25 standard deviations above the mean, which puts it at the 89.4th percentile (normalcdf (-100,1.25)).

9. In a normal distribution with mean 25 and standard deviation 7, what proportions of terms are less than 20?
10. .

(By calculator: normalcdf (-100,20,25,7)= 0.2375.)

11. What are the mean, median, mode, and standard deviation of a standard normal curve?
12. Answer: Mean = median = mode = 0. Standard deviation = 1.

13. Find the five-number summary and draw the modified box plot for the following set of data: 12, 13, 13, 14, 16, 17, 20, 28.
14. Answer: The five-number summary is [12, 13, 15, 18.5, 28]. 28 is an outlier (anything larger than 18.5 + 1.5(18.5 – 13) = 26.75 is an outlier by the 1.5(IQR) rule). Since 20 is the largest nonoutlier in the dataset, it is the end of the upper whisker, as shown in the following diagram:

.

15. A distribution is strongly skewed to the right. Would you prefer to use the mean and standard deviation, or the median and interquartile range, to describe the center and spread of the distribution?
16. Answer: Because the mean is not resistant and is pulled toward the tail of the skewed distribution, you would prefer to use the median and IQR.

17. A distribution is strongly skewed to the left (like a set of scores on an easy quiz) with a mean of 48 and a standard deviation of 6. What can you say about the proportion of scores that are between 40 and 56?
18. Answer: Since the distribution is skewed to the left, we must use Chebyshev's rule. We note that the interval given is the same distance (8) above and below = 48. Solving 48 + k(6) = 56 gives k = 1.33. Hence, there are at least % = 43.5% of the terms between 40 and 56.

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