Chapter 6. Univariate descriptive statistics 1. Compute the mode, median, and mean for the following four sets of numbers: Show
Use this set of numbers for the following questions:
2.Assume the numbers in the data are the answers you get when you ask people "How many magazines do you subscribe to?" What are the proper measures of central tendency and dispersion for this data? Calculate their values.
3. Assume the numbers in the data are the answers you get when you ask people "Name your favorite television program." Then you classify each program according to its thematic content. You use a system that has seven different classes (eg. 1=science fiction, 2=comedy, 3=romance, 4=adventure, 5=news, ....). The numbers in the data indicate which category their favorite programs fall into. What are the proper measures of central tendency and dispersion for this data?
4. Assume the numbers in the data are the answers you get when you ask people "What is your household's annual income? I'm going to read a list of possible ranges, and I want you to stop me when I read the range that describes your household's income." You then read the following list and record their answers:
What are the proper measures of central tendency and dispersion for this data? Calculate their values.
5. Below are the final exam scores in percentages for students in a course on postmodernist approaches to analysis of individual differences in skiing preferences.
a. Which of the measures of central tendency are the most and least appropriate for this data?
b. Which tell you more about the relative performance of males and females on the exam?
c. Discuss the benefits and drawbacks of each measure of central tendency for this data.
d. Compute the range, interquartile range, and standard deviation.
e. Discuss the benefits and drawbacks of each measure of dispersion for this data.
6. Use the table of random numbers (Table 7 in Appendix B) for this question. Use the last two digits of the 5-digit numbers. Starting at the top of the second column, scan down and mark the numbers that are between 10 and 29, including 10 and 29. Do this until you get a total of 15 numbers. Write these 15 two-digit numbers on a piece of
paper. Calculate the median, the mean, and the standard deviation for these numbers. Use the computational equation for standard deviation. 7. Analyze all four sets of numbers in Question 1 in terms of which of the measures of central tendency are the most and least appropriate. For each set of numbers, discuss the benefits and drawbacks of each measure of central tendency. 8. On a mid-term exam, the median score is 73 and the mean is 79. Which student's score is likely to be further away from the median — the one at the top of the class or the one at the bottom? Why?
9. If the standard deviation of a sample is 5.3,
10. Compute the standard deviation, range, and interquartile range for the following data:
11. Multiply each of the nine numbers in Question 11 a by a constant, say 0.4, and calculate the standard deviation. What is the effect on the standard deviation of multiplying the numbers by a constant? Try it with a different constant, say 1.3. What is the effect? What is the general pattern here?
12. Subtract a constant, say 50.0, from each of the nine numbers in Question 11, and calculate the standard deviation. What is the effect on the standard deviation of subtracting a constant? Try it with a different constant, say 63.89. What is the effect? What is the general pattern here?
13. What is the nature of the sample data if s = 0 and n = 75?
Which of the following are advantages of the variance compared to the range?Which of the following are advantages of the variance compared to the range? It uses all of the values in the data, not just two.
What is an advantage of using the range as a measure of variation?As a measure of variation, the range has the advantage of being easy to compute. Its disadvantage, however, is that it uses only two entries from the data set.
What is the main advantage of interpreting the standard deviation instead of the variance?Variance helps to find the distribution of data in a population from a mean, and standard deviation also helps to know the distribution of data in population, but standard deviation gives more clarity about the deviation of data from a mean.
Which of the following statements correctly describes the variance of a data set?Answer and Explanation: The correct answer to the given question is option d) is the average of the squared deviations from the mean. The variance of a given data set is determined by taking an average of the squared deviations of every observation from the mean value.
|