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 / 2 / 2 / 3 / 6 / 7 / 7 / 9 / 9 / 9 / 9
3 / 0 / 4 / 5

b) Use the stem and leaf display to find the quartiles , , and .

, the number in 11th position. , the average of the numbers in 5th and 6th positions. , the average of the numbers in 16th and 17th positions.

c) Determine the Interquartile range.

d) Complete the five-number summary diagram.

Minimum / Q1 / M / Q3 / Maximum

e) Complete the boxplot for this data.

2. Write down a list of three numbers so that the mode is 20, the median is 20, and the mean is 15.

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

Total

/ 75

a) Complete the relative frequency distribution.

Days of travel / Relative Frequency
0-6 / .20
7-13
14-20
21-27
28-34 / .03
35-41 / .01

Total

/ 1.00

b) Complete the histogram.

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?

b) 1.2 minutes late and 9.6 minutes late?

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?

6. The maximum heart rates after exercise for 9 people are recorded below.

a) Complete the following table.

Heart rate,
119 / 154 / -35 / 1225
130 / 154 / -24 / 576
145 / 154
150 / 154
155 / 154
160 / 154
165 / 154
170 / 154 / 16 / 256
192 / 154 / 38 / 1444

Total

/ 0

b) Find the sample variance using the formula, .

c) Find the sample standard deviation.

d) Find the range.

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?

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
Total / 125

How many specimens weigh

a) at most 59.9 grams? b) less than 40.0 grams? c) more than 100.0 grams?

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
Total / 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

Car A

/ 27.9 / 30.4 / 30.6 / 31.4 / 31.7
Car B / 31.2 / 28.7 / 31.3 / 28.7 / 31.3
Car C / 28.6 / 29.1 / 28.5 / 32.1 / 29.7

a) Find the mean miles per gallon for each of the three cars.

/ Mean mpg

Car A

Car B
Car C

b) Find the median miles per gallon for each of the three cars.

/ Median mpg

Car A

Car B
Car C

c) If the maker of Car A wants to advertise that its car performed the best, what measure should they use?

d) If the maker of Car B wants to advertise that its car performed the best, what measure should they use?

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:

a) Would you say that speed gain and weeks in program are positively correlated, negatively correlated, or uncorrelated?

b) Given that , , , , and , use the formula to find the value of the correlation coefficient.

c) Find the equation of the least squares regression line, , with the coefficients rounded to two places using the formulas and

.

d) Using the equation of the regression line, predict the speed gain of a student after 3 weeks in the program.

e) Determine the value of the coefficient of determination, and interpret it.