1. The mean diameter measurement of a Purdy Goode Compact Disc is 12 cm, with
a mean absolute deviation of 0.12 cm. No CDs can be shipped that are more than
one mean absolute deviation away from the mean. What is the range of diameters
of CDs that can be shipped?
2. The data in the table below represent the student-to-teacher ratios for the
elementary and secondary schools, listed by region, in the continental United
States.
Northeast
ME
NH
VT
MA
RI
CT
NY
PA
NJ
DE
MD
WV
13.9
16.2
13.2
15.4
15.4
13.6
14.6
17.0
15.6
13.6
16.8
16.5
Midwest
MI
WI
MN
OH
IN
IL
IA
MO
KY
ND
SD
NE
19.8
16.2
17.3
17.2
17.5
16.7
15.6
15.5
19.9
15.5
15.2
14.6
South
VA
NC
SC
GA
FL
AL
MS
TN
AR
LA
OK
TX
15.7
16.9
16.8
18.3
17.2
19.9
17.9
19.2
16.8
18.6
15.6
15.4
West
WA
OR
CA
NV
ID
UT
AZ
MT
WY
CO
NM
KS
20.1
18.5
22.8
19.4
19.6
25.0
19.4
15.9
14.5
17.8
18.1
15.0
Calculate the mean and the MAD for each region. What does this tell you about the
distribution of each set of ratios? Which region has the most consistent ratios?
3. The following information was collected during a mathematics lab by a group of
students. The mean measurement was 46.3 cm, and the devations of the eight
individual measurements were 0.8 cm, -0.4 cm, 1.6 cm, 1.1 cm, -1.2 cm, -0.3 cm,
-0.6 cm, and –1.0 cm.
a. What were the original eight measurements collected?
b. Find the MAD of the original measurements.
c. Which measurements were more than one mean absolute deviation form
the mean?
4. The students in four classes recorded their pulse rates. The class mean and the
MAD are given below. Each class has an equal number of students.
Class
1 period
3rd period
6th period
7th period
st
Mean
79.4
74.6
78.2
80.2
MAD
3.2
5.6
4.1
7.6
a. Which class has students with pulse rates most alike? How can you tell?
b. Can you tell which class has the students with the fastest pulses? Why or why
not?
c. Using the same scale for each class, sketch your best estimate of a box plot for
each class.