# Basic Statistics

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

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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#### Solution Summary

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