Liberty University BUSI 230 Core Competency Quiz complete solutions answers and more!

Liberty University BUSI 230 Core Competency Quiz complete solutions answers and more!

Look at the histogram below, which shows mileage, in miles per gallon (mpg), for a random selection of older passenger cars.

(a) Is the shape of the histogram essentially bimodal?

(b) Jose looked at the raw data and discovered that the 54 data values included both the city and highway mileages for 27 cars. He used the city mileages for the 27 cars to make the histogram below.

Using this information and the histograms shown above, construct a frequency table for the highway mileages of the same cars. Use class boundaries

Class Boundaries

Frequency

Another display technique that is somewhat similar to a histogram is a dotplot. In a dotplot, the data values are displayed along the horizontal axis. A dot is then plotted over each data value in the data set. For more details, view How to Make a Dotplot. The figure below shows a dotplot generated by Minitab for the number of licensed drivers per 1000 residents by state, including the District of Columbia (Source: U.S. Department of Transportation).

(a) From the dotplot, how many states have 600 or fewer licensed drivers per 1000 residents?

(b) About what percentage of the states (out of 51) seem to have close to 800 licensed drivers per 1000 residents? (Round your answer to one decimal place.)

(c) Consider the intervals 550 to 650, 650 to 750, and 750 to 850 licensed drivers per 1000 residents. In which interval do most of these states fall?

Certain kinds of tumors tend to recur. The following data represent the lengths of time, in months, for a tumor to recur after chemotherapy (Reference: D.P. Byar, Journal of Urology, Vol. 10, pp. 556-561).

For this problem, use five classes.

(b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Give relative frequencies to 2 decimal places.)

(c) Draw a histogram.

(d) Draw a relative-frequency histogram.

(e) Categorize the basic distribution shape.

(f) Draw an ogive. (Graph each point and the closed line segments connecting the points to create your graph.)

It is costly in both time and money to go to college. Does it pay off? According to the Bureau of the Census, the answer is yes. The average annual income (in thousands of dollars) of a household headed by a person with the stated education level is as follows: 24.5 if ninth grade is the highest level achieved, 41.6 for high school graduates, 59.6 for those holding associate degrees, 82.7 for those with bachelor's degrees, 100.9 for those with master's degrees, and 121.3 for those with doctoral degrees. Make a bar graph showing household income for each education level.

How do college professors spend their time? The National Education Association Almanac of Higher Education gives the following average distribution of professional time allocation: teaching, 55%; research, 16%; professional growth, 3%; community service, 11%; service to the college, 11%; and consulting outside the college, 4%. Make a pie chart showing the allocation of professional time for college professors.

The following ogives come from different distributions of 50 whole numbers between 1 and 60. Labels on each point give the cumulative frequency and the cumulative percentage of data.

(a) In which distribution does the most data fall below 20.5?

(b) In which distribution does the most data fall below 40.5?

(c) In which distribution does the amount of data below 20.5 most closely match that above 30.5?

(d) Which distribution seems to be skewed right?

Which distribution seems to be skewed left?

Which distribution seems to be mound-shaped?

How long did real cowboys live? One answer may be found in the book The Last Cowboys by Connie Brooks (University of New Mexico Press). This delightful book presents a thoughtful sociological study of cowboys in West Texas and Southeastern New Mexico around the year 1890. A sample of 32 cowboys gave the following years of longevity:

(a) Make a stem-and-leaf display for these data. (Use the tens digit as the stem and the ones digit as the leaf.)

Longevity of Cowboys

(b) Consider the following quote from Baron von Richthofen in his Cattle Raising on the Plains of North America: "Cowboys are to be found among the sons of the best families. The truth is probably that most were not a drunken, gambling lot, quick to draw and fire their pistols." Does the data distribution of longevity lend credence to this quote?