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Basic Statistics

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Part I T/F and Multiple Choice Questions

1. The mean, median, and mode are the most common measures of dispersion (spread). _____(T/F)

2. Each set of data has four quartiles; they divide the ranked data into four equal quarters.
_____ (T/F)

3. The standard score (or z-score) identifies the position of a particular value of x has relative to the mean, measured in standard deviations. _____ (T/F)

4. For any distribution, the sum of the deviations from the mean equals zero. _____ (T/F)

5. Ina data set, the mode will always be unique. _____ (T/F)

6. Correlation coefficients range between 0 and +1. _____ (T/F)

7. The line of best fit is used to predict the average value of y that can be expected to occur at a given value of x. _____ (T/F)

8. For which of the following situations is it appropriate to use a scatter diagram or scatter plot?
A. Presenting two qualitative variables
B. Presenting one qualitative and one quantitative variable
C. Presenting two quantitative variables
D. All of the above

9. The only measure of central tendency that can be found for nominal data is the
A. mean B. median C. mode D. midrange

10. The measure of central tendency that is most affected by a few large or small numbers is
A. mean B. median C. mode D. range

11. When a distribution is bell-shaped, approximately what percentage of data values will fall within one standard deviation of the mean?
A. 50% B 95% C. 68% D. 99.7%

Part II Short Answers and Computational Questions

1. What is the relationship between the variance and the standard deviation? What are the symbols used to represent the sample variance and standard deviation? Why is the unbiased estimator of variance used?

2. Nine households had the following number of children per household:

2, 0, 2, 2, 1, 2, 4, 3, 2

Find the mean, median, mode, and midrange for these data.

3. a) Use Chebyshev's theorem to find what percent of the values will fall between 120 and 150 for a data set with mean of 135 and standard deviation of 7.5.
b) Use the Empirical Rule to find what two values 95% of the data will fall between for a data set with mean 234 and standard deviation of 12.

4. Find P25 for the following data: 2 6 3 4 2 1 2 0 1 3 6 3

5. You are given the following frequency distribution for the number of errors 55 students made in a test

Errors Frequency
0-2 14
3-5 13
6-8 11
9-11 8
12-14 9
Find: a. mean b. variance c. standard deviation.

6. An aptitude test has a mean of 220 and standard deviation of 10. find the corresponding z score for: a) a test score of 232 b) a test score of 212

7. You are given the following data.

x y
2 14
3 13
4 11
5 8
5 9
7 4
7 3
a. SS(x)
b. SS(y)
c. SS(xy)
d. The linear correlation coefficient, r
e. The slope b1
f. The y-intercept, b0
g. The equation of the line of best fit.

8. The bar graph below compares the mean time in seconds for 7-yr old girls to complete a certain task to the mean time in seconds for 7-yr old boys to complete the same task. There is a statistical deception here. Explain what is deceptive about the bar graph.

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Solution Summary

The solution contains various statistics problem in the areas of Basic Statistics, Regression analysis and Empirical rule.

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1. Mr. Knight owned of a family business. He sold of the business to his sister. What portion of the business does he still own?
Rocco scored 81, 89, 68, 92, and 77 on his mathematics quizzes. Round each score to the nearest ten to estimate his total score.

3. A 2.41 pound oven roast costs $9.62. However, today there is a Manager's Special, and the roast is on sale for $2.39 per pound.
a) What is the sale price for the roast?
b) How much money would you save if you buy the roast today?

4. Multiply (-7.5)(9)(-7).
5. Find two factors of 60 with a sum of 17.
6. Janice has a 6% commission rate on all her sales. If she sells $80,000 worth of merchandise in 1 month, what commission will she earn?
7. On a test of 36 questions, Sam answered 16 correctly. On another test, Sam answered 32 correctly out of 72. Did Sam get the same portion of each text correct?
A railing for a deck requires pieces of redwood 5 ft 10 in., 7 ft 8 in., and 6 ft 2 in. long. What is the total length of material that is needed?

9. Paula's car payment is $342.37 per month for 3 years. How much will she pay for her car by the end of the third year?

10. Jamal is fencing a rectangular field that measures 31 ft by 26 ft. How much fencing should he buy?

11. Find the greatest common factor of 30, 45, and 50.
12. List all the prime numbers between 10 and 30.

13. Ms. Jefferson has been given a loan of $20,000 for 1 year. If the interest charged is $800, what is the interest rate on the loan?
14. Find the least common multiple of 9, 14, and 42
15. Subtract.

16. A block of cheese weighing 2.6 pounds (lb) sold for $15.55. Find the cost per pound to the nearest cent.

17. Carlos works 8.25 h and receives $102.30 pay. What will he receive at the same rate if he works 14 h?
18. Evaluate

19. Solve for the unknown:

20. The following scores were recorded on a 100-point examination:
95, 75, 76, 86, 96, 71, 65, 81, 95, 76, 69, 81, 93, 88, 94

Find a) the mean and b) the median examination scores.

21. Phil needs to practice free throws of an hour
each day. If he has already practiced
of an hour today, how many more minutes does he
need to practice?

A computer can execute 64 instructions per microsecond. How many instructions can it execute in 10 minutes?

23. Find the five-number summary of the following set of numbers.

0.16, 0.08, 0.27, 0.20, 0.22, 0.32, 0.25, 0.18, 0.28, 0.27

24. If $7,800 is deposited into an account paying 6% interest compounded annually (at the end of each year), how much money is in the account after 2 years?
25. Cindy is carpeting a recreation room 8 yd long and 6 yd wide. If the carpeting costs $18 per square yard, what will be the total cost of the carpet?
26. Express the partially shaded region as a) a decimal, b) a fraction, and c) a percent.

27. On the blueprint of Lauren's new office building, the scale is 3 in. equals 8 ft. What will be the actual length of Lauren's office if it measures 6 in. long on the blueprint?
28. Find the missing length of the right triangle.

29. Greg spent hour (h) responding to emails and h returning phone calls. How many minutes did he spend on the two activities?
The pie chart shows the distribution of a person's total yearly income of $44,000. Find the amount budgeted for utilities.
31. The interest rate on a mortgage was % last year. This year the interest rate is %. How many percentage points has the interest rate increased?
32. Perform the indicated operation.

33. The graph and table below show the income for a local company. Use this information to predict the income in the year 2005.

Year Total Income (in millions)
1980 $6.3
1985 $21.5
1990 $39.8
1995 $57.4
2000 $65.3

34. Are the following sets of numbers a perfect triple?

A. 7, 15, 18
B. 4, 5, 6
C. 7, 24, 25
35. A college basketball team scored 67, 75, and 69 points in three games. If its opponents scored 82, 62, and 55 points, by how much did the team outscore its opponents?

36. Automobiles and small trucks account for 84% of the travel to and from work in the United States. What fraction represents all other means of travel to and from work in the United States?

37. Find the area of the shaded part in the figure. Use 3.14 for and round your answer to one decimal place.

38. Find ma and mb.

39. If m 63, find the complement and supplement to .
40. Complete the statement.

A. 12 L = ________ qt
B. 13 oz = ________ g
C. 13 fl oz = ________ mL

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