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1. From March 1981 to February 1983 the number of burglaries committed each month in a Georgia town was recorded. They are given in the chart below. Between months 12 and 13 a law was enacted requiring citizens to own a gun. Town officials felt th
2.83
This is correct. There were thirty-four burglaries over this 12-month period, which gives an average of 2.83. Text reference: page 40 in Chapter 2.
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2. The following histogram represents the distribution of acceptance rates (percent accepted) among twenty-five business schools in 1998. In each class interval, the left endpoint is included but not the right.
Which statement is true?
The first quartile must be at least 15 but no larger than 22.5.
This is correct. The first quartile is the average of the sixth and seventh smallest observations (the median of the twelve smallest observations). From the histogram we know the interval 7.5
3. You receive a fax with six bids (in millions of dollars): 2.2, 1.3, 1.9, 1.2, 2.4, and x, where x, is some number that is too blurry to read. Without knowing what x is, the median
must be between 1.3 and 2.2.
This is correct. The median is the average of the third and fourth smallest observations. The third smallest must be at least 1.3. It will be 1.3 when x 1.3, or else it will be larger. It can't possibly be smaller than 1.3. Si
4. A sample was taken of the salaries of four employees from a large company. The following are their salaries (in thousands of dollars) for this year.
33 31 24 36
The variance of their salaries is
26.
This is correct. The mean of these numbers is 31, and the four deviations from the mean are 2, 0, -7, and 5. Squaring these deviations and adding them gives the sum of squared deviations to be 78. Divide by n - 1 = 3 to get the variance. Text referenc
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5. For a physics course containing eleven students, the maximum point total for the quarter was 200. The point totals for the eleven students are given in the stemplot below.
Which of the following statements is true about the stemplot?
We can compute the mean number of points for the eleven students from the information in the stemplot.
This is correct. The stemplot gives the individual observations, so it is possible to compute the value of any summary statistic from the stemplot. Text
Which of the following measures are not affected by outliers?
The IQR.
This is correct. The IQR measures the spread of the middle half (the distance between Q1 and Q3) so any outliers will not affect this measure. Text reference: pages 51-53 in Chapter 2.
7. Does the value of the standard deviation depend on the value of the mean?
Yes. You need to know the mean to be able to calculate the standard deviation.
This is correct. The variance, which is the square of the standard deviation, is the average squared distance from the mean. Text reference: pages 49-51 in Chapter 2.
8. A teacher gave a 25 question multiple choice test. After scoring the tests, she computed a mean and standard deviation of the scores. The standard deviation was 0. Based on this information,
all the students had the same score.
This is correct. The standard deviation measures the spread of the scores. If all the scores were the same, there is no spread, so the standard deviation will be 0. Text reference: pages 49-51 in Chapter 2.
9. The five-number summary of scores on a test is
35 60 65 70 90
Based on this information,
there are both high and low outliers.
This is correct. The 1.5
IQR criterion says outliers are more than 1.5
IQR below Q1 or above Q3. The IQR is 70 - 60 = 10, so 1.5*IQR is 15. Outliers will be 15 above 70 (above 85) or 15 below 60 (below 45) so both end
10. Total SAT scores for ten randomly selected students are:
1020 1260 1100 1260 1100 1020 960 1000 990 1160
The mean of these scores is
1087.
This is correct. Add all the observations together, then divide by how many observations there are (10), or use a calculator or other software. Text reference: pages 40-41 in Chapter 2.