AP Statistics – Chapter 1 Exercise Solutions & Explanations:
1.27 – Quiz Grades
a. 85.
b. 79.33. The mean is sensitive to outliers.
c. This would be a good situation to use a stem and leaf plot. Also, a histogram could be used using the given widths of the grading scales so show
the distribution of grades.
1.28 – SSHA scores
a. [Stemplot]. One potential outlier is 200. The center is 138.5. The scores range from 101 to 178, excluding 200, so the range is 77.
b. 141.056 = mean
c. 138.5 = median. The mean is larger than the median because of the extreme value 200 [mean is not resistant].
1.30 – Mean salary
a. The mean salary is $60,000. Seven of the eight employees earned less than the mean. The median is $22,000. An unethical reporter would
report the mean salary as “typical” or “average” salary.
1.32 – Home run records
a. Mean: 37.0. Median: 37.0. This leads towards the statement that the distribution is symmetrical [not skewed].
b. [Stemplot]
c. His “typical” number of home runs per year is 37; [2001 was very unusual].
1.37 – Bond’s home runs
a. Q1 = 25 and Q3 = 45
b. it is not an outlier [75 is the upper boundary for outliers]. Note: Is it necessary to say that 75 is the “upper boundary” for outliers?
1.39 – Phosphate levels
a. 5.4 mg/dl
b. 0.6419 mg/dl
c. Calculator results should agree with the answers from part (a) and (b).
1.40 – Choosing measures of center and spread
a. The median and IQR because the distribution is skewed to the right
b. The mean and standard deviation because the distribution is symmetric
c. The mean and standard deviation because the mean is roughly symmetric
1.42 – Median and mean: [Answers will vary] – Example: {1, 2, 10, 11, 11}
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1.45 – Raising teacher’s pay
a. The mean and median will both increase by $1000
b. No. The difference Q3 – Q1 will remain the same
c. No. The standard deviation remains unchanged
1.47 – Which AP exam is easier: Calc AB or Stats?
a. [Graph – could create a side-by-side bar graph]
b. The distribution of scores on the statistics exam is roughly symmetric with a peak at 3. The distribution of scores on the AP calculus exam has a
peak at 1 and another slightly lower peak at 5. It is impossible to tell which is “easier” from this.
1.49 – Who makes more?
a. [Histogram]
b. Both histograms are skewed to the right. The range of salaries is the same.
c. Roundoff error.
1.50 – Linear Transformations
a. Let Xnew = 746X. The mean, median, IQR, and standard deviation will all be multiplied by 746.
b. Let Xnew = (5/9)(X – 32). Multiply the old mean by 5/9 and subtract 160/9. The IQR and standard deviation will be multiplied by 5/9.
c. Let Xnew = X + 10. The mean and median will increase by 10. The IQR and standard deviation will remain the same.