Rounding Off, Descriptive Statistics

Rounding Off

1. State the Round-Off Rule as described in Section 3.3. You will use this rule to decide how many decimal places to round the answers in this project. If you have not noticed by now, rounding off is important; at the very least, it can make the difference between a correct and incorrect answer.

2. What is .0299 rounded to nearest tenth? See handout on rounding if you are having trouble.

3. What is .0299 rounded to nearest hundredth?

Descriptive Statistics

The following questions pertain to the height data in the file "project 1 data." [see end of Word file.]

4. Fill in the frequency distribution for the heights:

Height Frequency
60-62
63-65
66-68
69-71
72-74
75-77

5. Looking at the frequency distribution, do the heights seem to have a "normal distribution," as described in Section 2.2? Whether you answer yes or no, give a brief reason for your answer.

6. What is the mean of the data set? Use the round off rule above to determine how many decimals you need to show.

7. What is the mode?

8. What is the median?

9. Use Excel, Statcrunch, or STATDISK to find the sample standard deviation of the original data set. Use the round off rule to determine how many decimal places your answer should be.

10. Use the "Range Rule of Thumb", as described in Chapter 3, to estimate the sample standard deviation. Show your calculations so I know how you got your answer. Use two decimals.

11. What is the variance of the set? Use the round off rule to determine how many decimals to use.

12. The "Empirical Rule" from chapter 3 says that the percent of the data values that should fall within two standard deviations of the mean is:

13. Use the mean and the standard deviation values that you found above to compute the interval ( - 2s, + 2s). Make sure to write your answer as an interval: (a, b). Use one decimal place for each endpoint.

14. What percent of the height data values fall in this range? Give you answer in percent format with one decimal place, e.g. 32.0% or 98.2%. For example, if the interval you found in #13 was (63.2, 66.8) then the percent of data values falling in this interval is 19/30 = 26.7%. Is this value fairly close to what the Empirical Rule states? Highlight yes or no.

15. What is the z-score for the data value 5'9"? Don't forget to convert to inches. Show your calculation; make sure your answer seems reasonable. Use two decimal places. Use the same mean standard deviation you found above.

16. In section 3.4, the author finds the 20th percentile of the "best actresses' ages." Following the figure 3-6 flow chart, he computes . Why does he round 15.2 to 16 and use the 16th value in the list, instead of the 15th value?

17. Compute the 89th percentile of the height data. Show work (like the actress age example in the text book) so I know how you got your answer.

Data

Height in inches
60
60
60
63
63
63
63
63
63
63
63
63
63
63
64
64
64
66
66
66
66
66
69
69
69
70
70
72
72
75