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Basic Statistics

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
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.