Download Math 1342 Review 1

Math 1342 Review 1
1. The highway miles per gallon for 21 models of cars is recorded below.
22 27 29 35 29 22 19
26 34 29 22 30 19 22
23 27 29 22 19 19 20
a) Complete the following ordered stem and leaf display.
1
9
9
9
9
2
0
2
2
2
3
0
4
5
2
2
3
6
7
7
9
9
9
9
b) Use the stem and leaf display to find the quartiles Q1 , Q2 , and Q3 .
Q2  23 , the number in 11th position. Q1  21 , the average of the numbers in 5th and 6th
positions. Q3  29 , the average of the numbers in 16th and 17th positions.
c) Determine the Interquartile range.
IQR  Q3  Q1  29  21  8
d) Complete the five-number summary diagram.
Minimum
Q1
19
21
e) Complete the boxplot for this data.
0
10
M
23
20
Q3
29
Maximum
35
30
40
2. Write down a list of three numbers so that the mode is 20, the median is 20, and the mean is
15.
5,20,20
3. The number of days of travel of 75 business managers is recorded in the following frequency
distribution.
Days of travel Frequency
0-6
15
7-13
21
14-20
27
21-27
9
28-34
2
35-41
1
75
Total
a) Complete the relative frequency distribution.
Days of travel
Relative Frequency
0-6
.20
7-13
.28
14-20
.36
21-27
.12
.03
.01
1.00
28-34
35-41
Total
b) Complete the histogram.
30
25
20
15
10
5
0
0
7
14
21
28
35
42
4. An airline’s records indicate that its flights between two cities are on the average 5.4 minutes
late with a standard deviation of 1.4 minutes. According to Chebyshev’s Inequality, at least
what percentage of the flights between the two cities arrive anywhere between
a) 2.6 minute late and 8.2 minutes late?
5.4  2.6  2.8

2.8
1

 2 standard deviations  1  2 100%  75%
1.4
 2 
8.2  5.4  2.8
b) 1.2 minutes late and 9.6 minutes late?
5.4  1.2  4.2

4.2
1

 3 standard deviations  1  2 100%  88.8%
1.4
 3 
9.6  5.4  4.2
5. The mean score of a student on the first three tests is 81. How many total points must the
student score on the next two tests if the overall mean score is to be 85 points?
3  81  x
 85  243  x  425  x  182
5
6. The maximum heart rates after exercise for 9 people are recorded below.
a) Complete the following table.
2
xi  x
Heart rate, xi
x
 xi  x 
119
154
-35
1225
130
154
-24
576
145
154
81
9
150
154
16
4
155
154
1
1
160
154
6
36
165
154
170
192
Total
154
154
11
16
38
0
121
256
1444
3756
b) Find the sample variance using the formula, s 2 
 xi  x 
3756
 469.5
8
n 1
2
.
c) Find the sample standard deviation.
469.5  21.67
d) Find the range.
192  119  73
e) According to Chebyshev’s Theorem, at least 75% of the values must be within 2 standard
deviations from the mean, 154. What is the actual percentage for this data set?
2 standard deviations  2  21.67  43.34
154  43.34  110.66
154  43.34  197.34
 All the data values are within 2 standard deviations from the mean.
 100%
7. The weights of 125 mineral specimens are given below.
Weight(grams) Frequency
0-19.9
19
20.0-39.9
38
40.0-59.9
35
60.0-79.9
17
80.0-99.9
11
100.0-119.9
3
120.0-139.9
2
125
Total
How many specimens weigh
a) at most 59.9 grams?
19  38  35  92
b) less than 40.0 grams?
19  38  57
c) more than 100.0 grams?
Can't be determined.
8. Find the modal age, median age, and mean age of child occupants in car accidents from the
table below.
Age(years) Frequency
1
699
2
747
3
594
4
538
5
513
3091
Total
mode  2
The median is the number in the 1546 th position, which is 3 .
mean 
699  2  747  3  594  4  538  5  513 8692

 2.8
3091
3091
9. A consumer testing service obtained the following miles per gallon in 5 test runs with each
of three compact cars.
Test run #1 Test run #2 Test run #3 Test run #4 Test run #5
27.9
30.4
30.6
31.4
31.7
Car A
31.2
28.7
31.3
28.7
31.3
Car B
28.6
29.1
28.5
32.1
29.7
Car C
a) Find the mean miles per gallon for each of the three cars.
Mean mpg
Car A
30.4
Car B
30.24
Car C
29.6
b) Find the median miles per gallon for each of the three cars.
Median mpg
Car A
30.6
Car B
31.2
Car C
29.1
c) If the maker of Car A wants to advertise that its car performed the best, what measure
should they use?
mean
d) If the maker of Car B wants to advertise that its car performed the best, what measure
should they use?
median
10. Students taking a speed reading course produced the following gains in their reading speeds:
Weeks in the program Speed gain
2
50
4
100
4
140
5
130
6
170
6
140
7
180
8
230
Here is a scatterplot of the data along with the least squares regression line:
300
250
Speed gain
200
150
100
50
0
0
2
4
6
8
10
Weeks in program
a) Would you say that speed gain and weeks in program are positively correlated, negatively
correlated, or uncorrelated?
positively correlated
b)
 x  42 ,  y  1140 ,  x y  6670 ,  x  246 , and
  
xy   

to find the value
 y  182800 , use the formula r 
 x     y   
Given
that
i
i
2
i
i i
xi
i i
2
i
2
i
xi
n
yi
n
2
2
i
yi
2
n
of the correlation coefficient.
r
6670  421140
8
246  428
2
182800  1140
8
2

685
 .950907503
25.5  20350
c) Find the equation of the least squares regression line, ŷ  b1 x  b0 , with the coefficients
 x  y 
xi yi   i n  i
rounded to two places using the formulas b1 
and
2
  xi 
2
xi  n

y
x 


.
b 
b 
i
0
i
1
n


n


b1 
b0 


6670  421140
685
8

 26.8627451
2
246  428
25.5
1140
 42 
 26.8627451   142.5  141.0294118  1.470588225
8
 8 
yˆ  26.86 x  1.47
d) Using the equation of the regression line, predict the speed gain of a student after 3 weeks
in the program.
yˆ  26.86  3  1.47  82.05
e) Determine the value of the coefficient of determination, and interpret it.
2
r 2  .950907503  .904225079
The least squares regression line explains 90.4225079% of the variation in the data.