middle value of the ranked data, and the mode is the most
commonly occurring piece of data. 5. The correct range is
8 because the range is defined as the difference between
the highest and lowest values. 6. Since an outlier is either
much larger or much smaller than most of the data, it
causes the range to become larger.
Ex e r c i se s 7. 12, 11, 10; mean 9. 63, 52, no mode;
median 1 1 .5 .9 1 3 .1 2 5 15.15 17. Set C: 3.8, 6.7; Set
D: 28.3, 9.0; the range of Set C is 3.8 with a mean of 6.7,
while Set D has a range of 28.3 and a mean of 9.
- First player: .062, .300; Second player: .029, .302; the
second player had a slightly higher mean over the six
seasons and was more consistent as shown by the smaller
range. 21. Student A has a greater mean and a greater
median. 23a. Plant A: 5.8, 5.8, 5.4, 1.2; Plant B: 5.6, 5.5,
no mode; 2.9 b. Plant A: mean as there is no outlier;
Plant B: either mean or median, if you consider 7.2 to be
an outlier c. The greater data values are in the bottom
rows of a stem-and-leaf plot. Since more of the data is
concentrated near the bottom of the plot for Plant A than
for Plant B, Plant A has the greater mean. 25. The mean,
median, and mode will each decrease by that amount,
while the range will stay the same. If you subtract the
same number d from each set then the sum will decrease
by nd w here n is the number of data values. Therefore
when you divide the total by n, the mean will decrease by
d. s ~nnd = fj-d. For the median, the middle number
will d e c r e a s e by d. The mode will decrease by d. The
range, on the other hand, will remain the same since
(highest value -d)— (lowest value - d) =
highest - lowest. 27. mean: 2.8 m, median: 2.8 m,
mode: 2.8 m and 2.9 m, range: 0.7 m 29. 46.4 mi/h
Lesson 12-4 pp. 746-751
Go t It? 1a. 60, 75, 85, 95, 105 b. 5, 7, 15, 21, 53
2 ' Monthly Sales (millions of $)- I I I I I I I I I I I II I II I -
2 6 10 14 18 22 26 30 34
- The median tells you the middle value of the data.
So in Miami the monthly rainfall is below 4.5 in. for half
the months and above 4.5 in. for half the months. For
New Orleans the monthly rainfall is below about 5.3 in.
for half the months and above 5.3 in. for the other half
of the months. 4a. 60 b. No; since the percentile rank is
the percent of scores that fall at or below a given score
there is always at least 1 value associated with a given
value. There is no 0 percentile; the lowest score is the
first percentile.
Lesso n Ch eck
1.48, 54, 100, 188, 256
File Size (megabytes)
-*—I---------- 1 ---------- 1 ----------t—
0 100 200 300- 24, 27, 29.5, 31.5, 33
Daily Attendance
-—I— I— I— I— I— I— I— I— I— I— I—-
23 25 27 29 31 33
•— { i- Class B 4. the middle box 5. 88 6. 75%; the third
quartile is the value that divides the data so that about
75% of the data lies below and about 25% of the data
lies above. 7. No; the test is scored on point values from
0 to 100, whereas the percentile rank tells you how you
did in reference to the rest of the group.
Ex e r c i se s 9. 3.2, 4.2, 5, 6.15, 12
11. 100, 100, 101, 104, 105
13. Movie Ratings
-»—I------ 1 -------- 1 ------- 1 ------1— * -
1 2 3 4 5
- ii ii ii--------•
Camera Prices ($)
H----- 1 ----- 1 ------ 1 ----- 1 -----1—
0 100 200 300 400 50017.60 19. 90<x<94 21. 0 </i < 73.5 23. It could
also be equal to the maximum value, which could happen
if the top quarter of the scores all have the same value.- You can only find the median, which is the value at
the line in the box.
Lesson 12-5 pp. 753-759
Go t It? 1a. quantitative; numerical quantities
b. qualitative; not numerical 2a. Bivariate; th e re are tw o
variables, b. Univariate; there is only one variable.- No; if you are using a stratified sampling method, you
should sample at random from each group. 4. Answers
may vary. Sample: Do you prefer action movies or
documentaries? 5. Students who have e-mail may be
more likely to have a cell phone.
Lesso n Ch eck 1. systematic 2. random 3. stratified - quantitative 5. The words delicious and plain are
biased and might influence a respondent's answer. - Univariate data involve one variable and bivariate data
involve two variables.
Ex e r c i se s 7. qualitative 9. quantitative 11. univariate - univariate 15. stratified; not a good sample as it
assumes each town has a similar number of voters