Download Answers

Math 109!
Name: KEY
Exam 1
1. Calculate the the indicated Values for the frequency distribution table
a. Calculate the class width: 24 - 20 = 4
Height (in inches)
b. Calculate the midpoint for the second
class: (27 + 24)/2 = 25.5
Class
2. Calculate the cumulative and relative
frequency for the indicated classes.
Frequency, f
20 - 23
1
24 - 27
2
28 - 31
6
32 - 35
7
36 - 39
4
Income (in thousands of dollars)
Class
Frequency, f
Cumulative
Frequency
Relative
Frequency
20 - 23
1
1
0.05
24 - 27
2
3
0.10
28 - 31
6
9
0.30
32 - 35
7
16
0.35
36 - 39
4
20
0.20
20
!
1 of 4
Math 109!
3. Draw a histogram for the frequency table above
Exam 1
)"
)"
("
("
'"
&"
&"
%"
$"
#"
$"
#"
!"
$#*'"
$'*'"
$+*'"
%%*'"
%)*'"
4. Using the ogive chart below estimate the total size of the sample: ____________________
&#"
&!"
%#"
%!"
$#"
$!"
#"
!"
#'(#"
$$&(#"
$)*(#"
%%#(#"
%+$(#"
&&'(#"
&*&(#"
,,*(#"
#!#(#"
5. Using the sample dataset: [52 86 71 70 67 58 74 68 56] = [52 56 58 67 68 70 71 74 86], n
=9
a. Mean: 52 + 56 + 58 + 67 + 68 + 70 + 71 + 74 + 86 = 602, 602 ÷ 9 = 66.9
b. Median: n is odd so the middle value is the median, 68
!
2 of 4
Math 109!
c. Mode: There is no number that repeats itself - no mode.
Exam 1
d. Range: 86 - 52 = 34
6. For the following data set, approximate the sample standard deviation of text messages per
day. First fill in the missing values!
Text
Messages
(per day)
Midpoint
Frequency
x*f
78 - 88
83
1
83.0
-42.7
1821.6
1821.6
89 - 99
94
0
0.0
-31.7
1003.6
0.0
100 - 110
105
5
525.0
-20.7
427.7
2138.3
111 - 121
116
15
1740.0
-9.7
93.7
1405.5
122 - 132
127
15
1905
1.32
1.7424
26.136
133 - 143
138
7
966
12.32
151.7824
1062.4768
144 - 154
149
5
745
23.32
543.8224
2719.112
155 - 165
160
2
320
34.32
1177.8624
2355.7248
50
6284
a.
11528.88
= 125.7
b. s = 15.3
7. The average IQ of students in a particular calculus class is 110, with a standard deviation of
5. The distribution is roughly bell-shaped. Use the Empirical Rule to find the percentage of
!
3 of 4
Math 109!
Exam 1
students with an IQ above 120.
120 is 2 standard deviations from the mean - (120 - 100) ÷ 5 = 2. According to the
empirical rule there is 97.5% of the sample below 2 standard deviations below this point.
So there must be 2.5% of the sample with a IQ score above 2 standard deviations.
8. Adult IQ scores have a bell-shaped distribution with a mean of 100 and a standard
deviation of 15. Use the Empirical Rule to find the percentage of adults with scores
between 70 and 130.
70 is 2 standard deviations below the mean and 130 is 2 standard deviations above the
mean. According to the empirical rule there is 95% of the population is between 2 standard
deviations above and below the mean.
9. The weights (in pounds) of 30 preschool children are listed below.
a. Find Q1: The middle value of the lower half is 28
!
Row
Value
Value
1
25
31
2
25
31
3
26
32
4
26.5
32.5
5
27
32.5
6
27
33
7
27.5
33
8
28
34
9
28
34.5
10
28.5
35
11
29
35
12
29
37
13
30
37
14
30
38
15
30.5
38
b. Find Q2: (30.5 + 31) ÷ 2 = 30.75
c. Find Q3: The middle value of the upper half is 34
d. What is the range of the data: 38 - 25 = 13
4 of 4