1. The following data give the hours spent studying per week by nine students. 12
16
7
22
11
18
7
25
16
Find the mean, median, and mode.
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. The following data give the hours spent studying per week by a sample of nine students. 12
16
7
22
11
18
7
25
16
Find the range, variance, and standard deviation. 4. Suppose the following data give the amount (in inches) of snowfall for 10 days during the months of January to March of 2004 for the state of Utah. 8
5
11
3
9
10
2
4
6
4
Find the range, variance, and standard deviation. 5.
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 Calculate the mean, variance, and standard deviation.
f 12 18 11 6 3
6.The following table gives the frequency distribution of auto insurance premiums (in hundreds of dollars) paid annually by a sample of 100 auto drivers. Annual Auto Premium ($00s) 2 to less than 4 4 to less than 6 6 to less than 8 8 to less than 10 10 to less than 12 12 to less than 14
f 3 19 28 25 16 9
Calculate the mean, variance, and standard deviation. 7. 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.
8.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
Make a box-and-whisker plot.
Answer 1. Mean = 134 ÷ 9 = 14.89 hours, Median = 16 hours, Mode = 7 and 16 hours
2. Mean = 117 ÷ 7 = 16.71 patients, Median = 16 patients This data set has no mode. 3. Range = 25 – 7 = 18 hours 2308 (134) 2 / 9 2308 1995.111 Variance = = 39.111 8 8 Standard deviation = 39.11 = 6.254 hours 4. Range = 121 2 = 9 inches 472 (62) 2 / 10 472 384.4 Variance = = 9.733 9 9 Standard deviation = 9.733 = 3.12 inches
5. Mean =
950 = 19 50
24,650 (950) 2 / 50 24,650 18,050 = 132 50 50 Standard deviation = 132 = 11.49
Variance =
818 = 8.18 100 7356 (818) 2 / 100 7356 6691.24 Variance = = 6.715 99 99 Standard deviation = 6.715 = 2.591
6. Mean =
7. a. First quartile = 33, Second quartile = 45, Third quartile = 51 b. 80th percentile = 51 c. 53.33% 8. Median = 45, First Quartile = 35.50, Third Quartile = 49, IQR = 49 – 35.5 = 13.5 Lower Inner Fence = 35.5 – 1.5(13.5) = 15.25 Upper Inner Fence = 49 + 1.5(13.5) = 69.25 Smallest value within the two inner fences = 29 Largest value within the two inner fences = 56
| --------- | --------- | -------- | --------- |--------- | -------- | --------- | 25 30 35 40 45 50 55 60