Chapter 1

 

 1. In 1988 there were 1,436 two-year colleges in the United States, of which 984 were public institutions.

      What is the relative frequency of public two-year colleges?

 

 2. Here is a frequency table for the hour at which the first flash of lightning each day was observed in a   

     study in Colorado. (Hour 1 stands for midnight to 1 am, and so on.)

 

    

            a.) Make a histogram of these data.

            b.) Describe the distribution: Is it roughly symmetric or distinctly skewed? Where is the center? At

                  what time of day does the first flash most often occur? Are there any outliers?

 

 3. Here is a table of the number of operations performed by each of a group of Swiss doctors. The data are

     recorded separately for male and female doctors.  

             

 

a.)    Make a stemplot of the entire data set. Describe the distribution: Is it symmetric or skewed?

       Where is  the median (half of the doctors perform more operations than this and half perform 

        less)? Are there any outliers?

            b.) Make a back-to-back stemplot to compare male and female doctors. What is the most obvious

                 difference between the two distributions?

 

 4. A survey of the hourly wages earned by students working part-time during the school year produces

     data such as $4.35, $5.50, $7.10, and $4.85. Show how you would truncate data such as these to make a

      stemplot by writing the stems and leaves for these four observations on a small stemplot.

 

 5. Anthropologists use the distribution of skull measurements to help classify ancient human remains.

     Here are measurements (in mm) on the forehead breadth of 12 skulls of the same type:

        122  124  127  121  121  113  130  131  117  128  111  115

     a.) Calculate the mean and the standard deviation of this distribution.

 

 6.  Problem #3 reports the number of operations performed by each of 26 Swiss doctors.

a.)    Find the five-number summary of this distribution (ignore the distinction between male and

female doctors.)

            b.) Are the two extreme observations classified as outliers by the 1.5 x IQR criterion?

 

 7. Answer the following questions:

            a.) The distribution of income in a large group is usually strongly skewed to the right. The median

                 household income in the U.S. was $29,943 in 1990. Was the mean family income larger or

                 smaller? Why?

b.)    A report on the distribution of fill weights for cola bottles says that, "The variation was very

      small; in fact, the standard deviation of weight for the 25 bottles was only s = - 0.12 grams."

      What is wrong with this statement? 

 

 8. The following is the density curve of the distribution of the time to failure of an electronic component.

            a.) What is the area under this curve?

            b.) Which of the two points marked on the curve is the mean and which is the median? Explain your

                 choice.

 

         

9. Scores on the Wechsler Adult Intelligence Scale ( a standard "IQ test") for the 20 to 34 age group are

      approximately normally distributed with mean 110 and standard deviation 25.

            a.) About what percent of people in this age group have scores above 110?

            b.) About what percent have scores above 160?