Review the following concepts if necessary:

- Graphical Analysis for AP Statistics
- Histogram for AP Statistics
- Measures of Center for AP Statistics
- Measures of Spread for AP Statistics
- Position of a Term in a Distribution for AP Statistics
- Normal Distribution for AP Statistics

### Rapid Review

- Describe the
*shape*of the histogram below: - 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?
- 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?
- A distribution of quiz scores has = 35 and
*s*= 4. Sara got 40. What was her*z*-score? What information does that give you? - In a normal distribution with mean 25 and standard deviation 7, what proportions of terms are less than 20?
- What are the mean, median, mode, and standard deviation of a
*standard normal curve?* - 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.
- 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?
- 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?

.

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

*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.

*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.

### Answer:

- .

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)).

.

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

*Answer:* Mean = median = mode = 0. Standard deviation = 1.

*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:

.

*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.

*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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