1At Center Hospital there is some concern about the high tur

1.At Center Hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses were as follows.

(a) Select the box-and-whisker plot of the data.

(b) Find the interquartile range.

2. What percentage of the general U.S. population have bachelor\'s degrees? The Statistical Abstract of the United States, 120th Edition, gives the percentage of bachelor\'s degrees by state. For convenience, the data are sorted in increasing order.

(a) Select the box-and-whisker plot.

(b) Find the interquartile range.
IQR =  

(c) Illinois has a bachelor\'s degree percentage rate of about 26%. Into what quartile does this rate fall?

Q₁between Q₁ and the median    Q₃above Q₃

3. Consumer Reports rated automobile insurance companies and gave annual premiums for top-rated companies in several states. The figure below shows box plots for annual premiums for urban customers (married couple with one 17-year-old son) in three states. The box plots were all drawn using the same scale on a TI-84Plus/TI-83Plus calculator.

(a) Which state has the lowest premium? the highest?

lowest, California; highest, Texaslowest, Texas; highest, Pennsylvania    lowest, Pennsylvania; highest, Californialowest, California; highest, Pennsylvania

(b) Which state has the highest median premium?

TexasPennsylvania    California

(c) Which state has the smallest range of premiums? the smallest interquartile range?

smallest range, California; smallest IQR, Texassmallest range, California; smallest IQR, Pennsylvania    smallest range, Texas; smallest IQR, Pennsylvaniasmallest range, Pennsylvania; smallest IQR, California

(d) The other set of figures give the five-number summaries generated on the TI-84Plus/TI-83Plus calculators for the box plots. Match the five-number summaries to the appropriate box plots.

Texas (a); California (b); Pennsylvania (c)Texas (a); Pennsylvania (b); California (c)    Pennsylvania (a); Texas (b); California (c)California (a); Pennsylvania (b); Texas (c)

4. Some data sets include values so high or so low that they seem to stand apart from the rest of the data. These data are called outliers. Outliers may represent data collection errors, data entry errors, or simply valid but unusual data values. It is important to identify outliers in the data set and examine the outliers carefully to determine if they are in error. One way to detect outliers is to use a box-and-whisker plot. Data values that fall beyond the limits

Lower limit: Q₁ ? 1.5 ? (IQR)
Upper limit: Q₃ + 1.5 ? (IQR)

where IQR is the interquartile range, are suspected outliers. In the computer software package Minitab, values beyond these limits are plotted with asterisks (*). Students from a statistics class were asked to record their heights in inches. The heights (as recorded) were as follows.

(a) Make a box-and-whisker plot of the data.

(b) Find the value of the interquartile range (IQR).
IQR =  

(c) Multiply the IQR by 1.5 and find the lower and upper limits. (Enter your answers to one decimal place.)

(d) Are there any data values below the lower limit? Above the upper limit? List any suspected outliers. What might be some explanations for the outliers?

Yes, 4 is below the lower limit and is probably an error.

Yes, 80 is above the upper limit and is probably an error.    

No, there does not appear to be any outliers.

5. Consider the following.

(a) What measures of variation indicate spread about the mean? (Select all that apply.)

variance

standard deviation

coefficient of variation

mean

(b) Which graphic display shows the median and data spread about the median?

5-number summary

histogram    

box-and-whisker plot

frequency chart

6.

Look at the two histograms below. Each involves the same number of data. The data are all whole numbers, so the height of each bar represents the number of values equal to the corresponding midpoint shown on the horizontal axis. Notice that both distributions are symmetric.

(a) Estimate the mode, median, and mean for each histogram.

(b) Which distribution has the larger standard deviation? Why?

Distribution (i), because more of the data are farther from the mean.Distribution (ii), because more of the data are farther from the mean.    Distribution (i), because more of the data are closer to the mean.Distribution (ii), because more of the data are closer to the mean.

7.

An elevator is loaded with 13 people and is at its load limit of 2405 pounds. What is the mean weight of these people? (Round your answer to one decimal place.)
lb

8. Which average - mean, median, or mode - is associated with the standard deviation?

mean

median    

mode

9. One standard for admission to Redfield College is that the student must rank in the upper quartile of his or her graduating high school class. What is the minimal percentile rank of a successful applicant?

10. Clayton and Timothy took different sections of Introduction to Economics. Each section had a different final exam. Timothy scored 83 out of 100 and had a percentile rank in his class of 72. Clayton scored 85 out of 100 but his percentile rank in his class was 70. Who performed better with respect to the rest of the students in the class, Clayton or Timothy? Explain your answer.

Clayton, since his score is higher.

Clayton, since his percentile score is lower.    

Timothy, since his score is lower.

Timothy, since his percentile score is higher.

11. Professor Cramer determines a final grade based on attendance, two papers, three major tests, and a final exam. Each of these activities has a total of 100 possible points. However, the activities carry different weights. Attendance is worth 6%, each paper is worth 7%, each test is worth 15%, and the final is worth 35%.

(a) What is the average for a student with 62 on attendance, 98 on the first paper, 100 on the second paper, 96 on test 1, 63 on test 2, 72 on test 3, and 71 on the final exam? (Round your answer to one decimal place.)


(b) Compute the average for a student with the above scores on the papers, tests, and final exam, but with a score of only 23 on attendance. (Round your answer to one decimal place.)

Solution

Min. 1st Qu. Median Mean 3rd Qu. Max.
2.00 10.25 23.00 20.65 28.25 42.00

the interquartile range = Q3-Q1
=28.25-10.25
=18