Measures of central tendency

Week 2 Practice Worksheet

Provide a response to the following prompts.

1. The Wilcox & Keselman (2003) article from this week’s electronic readings discusses two problems with measures of central tendency: skewness of the data and outliers. Discuss each of these issues and how they affect measures of central tendency.

2. How do the sample mean and the population mean differ? What is the symbol for each type of mean?

3. An expert reviews a sample of 10 scientific articles (n = 10) and records the following numbers of error in each article: 0, 4, 2, 8, 2, 3, 1, 0, 5, and 7.

a. Compute the mean, median, mode, sum of squares (SS), the variance, and the standard deviation for this sample using the definitional and computational formulas. You may use Microsoft® Excel® data anlysis to compute these statistics and copy your output into this worksheet.

Explain, to a person who has never had a course in statistics what you have done.

b. Note the ways in which the means and standard deviations differ, and speculate on the possible meaning of these differences, presuming they are representative of U.S. governors and large corporations’ CEOs in general.

4. A researcher records the levels of attraction for various fashion models among college students. He finds that mean levels of attraction are much higher than the median and the mode for these data.

a. What is the shape of the distribution for the data in this study?

b. What measure of central tendency is most appropriate for describing these data? Why?

5. On a standard measure of hearing ability, the mean is 300, and the standard deviation is 20. Provide the Z scores for persons whose raw scores are 340, 310, and 260. Provide the raw scores for persons whose Z scores on this test are 2.4, 1.5, and -4.5.

6. Using the unit normal table, find the proportion under the standard normal curve that lies in the tail for each of the follow useing table starting on page 673 (Hint: Remember to change all percents to decimals):

a. Z = 1.00

b. Z = -1.05

c. Z = 0

d. Z = 2.80

e. Z = 1.96

7. Suppose the scores of architects on a particular creativity test are normally distributed. Using a normal curve table (pp. 673-676 of the text), what percentage of architects have Z scores

a. above .10?

b. below .10?

c. above .20?

d. below .20?

e. above 1.10?

f. below 1.10?

Is this sample design an example of random sampling? Explain.

Assuming that all students attend his class that day, how many students will the instructor select to complete his questionnaire?

9. Suppose you were going to conduct a survey of visitors to your campus. You want the survey to be as representative as possible.

a. How would you select the people to survey?

b. Why would that be your best method?

10. In a school band, 9 kids play string instruments, 10 kids play woodwind instruments, 7 kids play brass instruments, and 4 kids play percussion instruments.

a. What is the probability that you randomly select a kid who plays a string or percussion instrument?

b. What is the probability that you randomly select a kid who does not play a brass instrument?

Measures of central tendency

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