MAT 115 – Basic Mathematics

Week #7 Checkpoint Chapter 8

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Instructions: For each assigned problem show your complete solution in the left column under each problem. Show all work for each problem (using either MathType or Equation Editor) in order to receive credit. Check calculations using a calculator. Be sure to reduce all fractions to lowest terms and include the appropriate units or percent signs if needed. If there is no work to show then explain in words how you solved the problem. Points will be deducted if there is insufficient explanation or work.

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Problems
(Enter your work and answer in this column) / Instructor’s comments
Section 8.1 –pp. 600–602, # 14, 18, 20, 24, 36
14. (1 pt)Find the median:
1, 4, 9, 15, 25, 36
Median is the term at the center. Since 9 and 15 are both at the center we will get the average of these two numbers as the median:

18. (1 pt)Find the mode:
41, 43, 56, 67, 69, 72
Mode is the term that has the highest frequency in the data. For this set there is no mode. No number appears twice.
20. (1 pt)Find the mode:
9, 8, 10, 9, 9, 10, 8
Mode is the term that has the highest frequency in the data. For this set mode is 9. It appears 3 times.
24. (2 pts)Statistics. A salesperson drove 238, 159, 87, 163, and 198 miles (mi) on a 5-daytrip. What was the mean number of miles driven per day?

36. (3 pts)Business and finance. The following scores were recorded on a 200-point final examination:
193, 185, 163, 186, 192, 135, 158, 174,
188, 172, 168, 183, 195, 165, 183
(a) Find the mean final examination score.
Total = 2640

(b) Find the median final examination score.
In ascending order: 135, 158, 163, 165, 168,172, 174, 183, 183, 185, 186, 188, 192,193, 195
Median is the middle term which is 183.
(c) Is the mean or median a more useful representative of the final examinationscores? Write a brief paragraph justifying your response.
I think median is a more useful representative of the final examination scores. Because there are very low and very high scores like 135 and 195. Mean is sensitive to these outliers but median is not.
Section 8.2 –p. 612,#2, 4, 6, 8, 10
Refer to the table on p. 606:
Round answers to the nearest tenth or tenth of a percent.
2. (2 pts)Please include units.
(a) What was the population in Europe in 2000?
510,000,000
(b) What is the total land area of Europe?
3,800,000 mi2
4. (1 pt)Compare the population per square mile in Asia to the population per square milein North America for the year 2000.
Asia: 4,028,000,000/17,400,000 = 231.5
N. America: 305,000/9,400,000 = 0.032
Population density in Asia is higher than North America
6. (2 pts)What is the percent increase in the population for all six inhabited continents, combined, excluding Asia, from 1950 to 2000?
Total in year 1950 = 2,556,000,000 - 1,591,000,000 = 965,000,000
Total in year 2000 = 6,279,000,000 - 4,028,000,000 = 2,251,000,000
Increase = 1,286,000,000
Percent increase = 1,286,000,000/965,000,000
= 1.33
= 133%
8. (1 pt)What was the percent increase in the population in South America from 1900 to2000?
Increase = 515,000,000 - 38,000,000 = 477,000,000
Percent increase = 477,000,000/38,000,000
= 12.55
= 1255%
10. (3 pts)
(a) What was the mean population of the six continents or land masses that werehabitable in 2000?
Total population = 6,279,000,000
Mean = 6,279,000,000/6
= 1,046,500,000
(b) What was the mean population in 1950?
Total population = 1,600,000,000
Mean = 1,600,000,000/6
= 266,666,667
(c) What was the percent increase in the mean population from 1950 to 2000?
Increase = 1,046,500,000 - 266,666,667
= 779,833,333
Percentage increase = 779,833,333/266,666,667
= 2.924
= 292.4%
Section 8.3 –pp. 623–624, #6, 8, 10
Use the graph below, showing the number of robberies in a town during the last 6 monthsof a year, for exercises 6 and 8.

6. (1pt)How many robberies occurred in November?
We find Nov. in the horizontal axis and draw a vertical line. The line hits the graph at point 4. So the number of robberies is 400.
8.(1 pt)What was the mean number of robberies per month over the last 6 months?

10.(1 pt)The graph and table below give the monthly principal and interest payments fora mortgage from 1999 to 2004. Use this information to predict the payment for2005.

It seems from the graph that there is an increasing trend and the payment for 2005 will be around 754 assuming the same increase in year 2004.
Section 8.4 –pp. 633–634, #2, 6, 10, 14
2.(2 pts)The table below gives the median earnings of women aged 25 and older who work full-time, year round, by educational attainment, according to the 2000 census.

Create a bar graph from this information.

6.(1 pt)The following pie chart shows the budget for a local company. The total budget is $600,000.Find the amount budgeted in Operating expenses.

0.20 x $600,000 = $120,000
10.(1 pt)The following pie chart shows the distribution of a person’s total yearly income of $24,000.Find the amount budgeted for utilities.

0.05 x $24,000 = $1,200
14.(2 pts)The following table gives the number of Senate members with military service in the 106th U.S. Congress, by branch.

Construct a pie chart from this information.

Section 8.5 –pp. 641–646, #4, 20, 38
4. (1 pt)Find the median:
26, 30, 38, 67, 59, 21, 17, 85, 22, 22
In ascending order,
17, 21, 22, 22, 26, 30, 38, 59, 67, 85
Median is the number in the middle. There are two numbers in the middle so the median is the average of these two numbers.

20. (2 pts)Give the five-number summary:
7, 7, 5, 4, 1, 9, 8, 8, 8, 5, 2
In ascending order: 1, 2, 4, 5, 5, 7, 7, 8, 8, 8, 9
Min = 1
1st quartile = 4
Median = 7
3rd quartile = 8
Max = 9
So the five number summary is as follows:
(1, 4, 7, 8, 9)
38. (1 pt)One measure used to describe a data set is the range. The range of a data set is given by thedifference between the max and the min of the set. The range describes the variability of thedata (that is, how much do the numbers vary).
Range =max –min
Find the range:
7, 7, 5, 4, 1, 9, 8, 8, 8, 5, 2
Min = 1
Max = 9
Range = 9 - 1 = 8

Mat 115 Week #8 Checkpoint