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Basic Statistics

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Part I T/F and Multiple Choice Questions

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

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

3. In a data set, the mode will always be unique. _____ (T/F)

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

5. 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)

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. 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%

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. 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

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. Find P25 for the following data: 1 4 5 4 3 2 1 3 4 5 4 0

3. An aptitude test has a mean of 101 and standard deviation of 9. find the corresponding z score for: a) a test score of 127 b) a test score of 80

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

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

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

5. a) Use Chebyshev's theorem to find what percent of the values will fall between 58 and 82 for a data set with mean of 70 and standard deviation of 4.

b) Use the Empirical Rule to find what two values 95% of the data will fall between for a data set with mean 152 and standard deviation of 11.

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

Errors Frequency
0-2 11
3-5 14
6-8 9
9-11 4
12-14 7
Find: a. mean b. variance c. standard deviation.

7. You are given the following data.

x y
2 14
3 9
4 11
5 11
5 10
7 5
7 4
Find
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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2.
Rocco scored 81, 89, 68, 92, and 77 on his mathematics quizzes. Round each score to the nearest ten to estimate his total score.

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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?
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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?

22.
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?
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Year Total Income (in millions)
1980 $6.3
1985 $21.5
1990 $39.8
1995 $57.4
2000 $65.3

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A. 7, 15, 18
B. 4, 5, 6
C. 7, 24, 25
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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
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C. 13 fl oz = ________ mL

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