Numerical Descriptive Measures
1. The mean is a measure of central tendency, but outliers influence it. This is a disadvantage. Illustrate this point with an example. 2. The following data give the number of patients admitted to a hospital on seven days during January 2003. 19 14 9 25 21 13 16 Find the mean and median. Do these data have a mode? 3. Consider the following two data sets: Data set I: Data set II:
18 23
26 31
14 19
37 42
58 63
Notice that we have added 5 to the value of each element of the first data set to obtain the corresponding values for the elements in second data. Calculate the mean for each of these two data sets. Comment on the relationship between the two means. 4. The mean number of cups of coffee consumed by 25 males is 4.4 and by 20 females is 3.5. Find the combined mean for males and females. 5. The mean weight (in pounds) at birth of seven babies is 8.6 pounds. The weights of six of these seven babies are 9.5, 7.4, 6.8, 10.6, 7.5, and 11.3 pounds. Find the weight of the seventh baby. 6. The mean weekly salary of 50 workers is $755. What is the sum of the weekly salaries of these 50 workers? 7. Outliers influence the range, as a measure of spread. This is a disadvantage. Illustrate this point with an example. 8. When is the value of the variance for a data set zero? Give one example of such a data set. Make the calculations and show that the variance for that data set is zero. 9. When is the value of the standard deviation for a data set zero? Give one example of such a data set. Make the calculations and show that the standard deviation for that data set is zero. 10. The following data give the hours spent studying per week by a sample of nine students. 12
16
7
22
11
18
Find the range, variance, and standard deviation. 11. Consider the following two data sets: Data set I: Data set II:
18 23
26 31
14 19
37 42
58 63
7
25
16
Notice that we have added 5 to the value of each element of the first data set to obtain the corresponding values for the second data set. Calculate the standard deviation for each of these two data sets using the sample formulas. Comment on the relationship between the two standard deviations. 12. The following table gives the frequency distribution of the values (in thousands of dollars) of cars owned by all 50 employees of a company. Value of Car ($000s) 0 to less than 10 10 to less than 20 20 to less than 30 30 to less than 40 40 to less than 50
f 12 18 11 6 3
Calculate the mean, variance, and standard deviation.
13. The following data give the time (in minutes) taken by 15 students to complete a finance test. 45 29
53 38
29 46
33 51
39 47
47 51
56 38
32
a. Calculate the values of three quartiles. b. Find the (approximate) value of the 80th percentile. c. Find the percentile rank of 46. 14. The following data give the time (in minutes) taken by 15 students to complete a finance test. 45 29
53 38
29 46
Make a box-and-whisker plot.
33 51
39 47
47 51
56 38
32