EXERCISES AND PROJECTS

Exercise 15-1

Here is a frequency distribution displaying grouped data on the percentage of voting-age persons registered to vote in 162 counties. Determine the median percentage of voter registration.

Percent Voter Registration f (counties)
0-9% 2
10-19 6
20-29 4
30-39 16
40-49 26

Percent Voter Registration f (counties)
50-59 36
60-69 32
70-79 27
80-89 11
90-100 2

Median percentage: ________

The League of Women Voters is planning to conduct voter registration drives in those counties which are in the lowest third in terms of the percent of voting-age persons registered to vote. What is the highest voter-registration percentage a county could have in order to qualify for a registration drive?
___________________

Exercise 15-2

Below is a list of 25 individuals and their hypothetical ratings on a "political ideology" scale ranging from a score of 1 (very liberal) to 10 (very conservative).

Abe (7) Mali (10)
Beth (6) Nico (1)
Chuck (7) Owen (4)
Darrell (3) Petra (8)
Elliott (5) Reagan (7)
Faith (6) Sal (7)
Gary (8) Tim (4)
Hal (7) Victor (7)
Issac (4) Will (4)
Jessica (7) Yulia (6)
Karl (8) Yazmin (9)
Linda (6) Zed (5)

Based upon these scores, determine the following:

  1. Mode __________
  2. Mean __________
  3. Standard deviation _________
  4. Standard score (Z) for Issac _______________
  5. Is this distribution positively or negatively skewed? Explain your answer.
    ______________________________________________________________________________
    ______________________________________________________________________________

Exercise 15-3

The Democratic Campaign Committee of the U.S. House of Representatives provided financial assistance in 2006 to Democratic candidates seeking election in "competitive" districts. The committee defined a competitive district as one in which the Democratic share of the 2002 vote was between 45 and 55 percent. Research assistants to the committee have found that the Democratic vote in 2002 had a mean of 52 percent and a standard deviation of 8.3. Assuming a normal distribution, determine the percentage of House districts that were "competitive" in 2002 and in which Democratic candidates received financial assistance.

Exercise 15-4

a. On the basis of the following set of sample data, calculate an appropriate measure of central tendency to determine whether men or women donated blood more frequently

Men Women


Number of Donations f Number of Donations f
1 36 1 27
2 18 2 21
3 14 3 18
4 9 4 2
5 6 5 6
6 2 6 7
____________
108 117

b. Using the data above, determine whether there is a greater variability in the amount of blood donation among men or among women.
c. Using the data above, group the data into intervals 2 units wide. Then calculate the mean, median, and standard deviation for the two samples. Why do you get different values from those calculated in (a) and (b) above?

Exercise 15-5

Which of the following two classes is more racially heterogeneous (has more racial variability)? Base your conclusions on an appropriate measure of dispersion.

Class X Class Y


Race f Race f
Caucasian 21 Caucasian 16
African American 8 African American 4
Native American 2 Asian American 4
Asian American 3
_______ _______
34 24

Calculate the coefficient of variation for the male and female distributions given above.

Exercise 15-6

Using the following set of values, (1) construct a frequency distribution, (2) construct a percentage distribution, (3) determine the interquartile range for the distribution, and (4) determine the median weight for this group. (Use appropriate interval widths.)

Weights of 32 New Members of TOPS (Take Off Pounds Sensibly)

203 142 169 188 128 267 153 122 180 216 194 118 134 202 198 155
176 188 166 233 175 145 133 109 118 157 130 193 124 111 109 126

Project 15-7

Do a brief study of your transportation usage for a few days. Keep track of how much time you spend on each trip and what type of transportation you take (don't forget walking if you use it to get to anyplace that might be reached by some other method of transportation).

  1. Once you have collected sufficient data on, say, 20 or more trips, calculate the mean and median time spent on your trips. Now calculate the variance and standard deviation for these data. You might find it interesting to compare these statistics with those of your friends or classmates.
  2. Construct a percentage distribution to indicate what percentage of your trips involve each mode of transportation. Determine how much variability there is in your use of transportation.