Solutions Hmwk

ISDS-361AExercises 1. Mean, average, Mode, Range, Variance & SD Panayiotis Skordi 1. A basketball game player has the quest points for seven games 20, 25, 32, 18, 19, 22, 30 Compute the following measures of central location a. mean b. median c. mode Answers a. Meanpic b. Medianpic c. Mode There is no mode. 2. conceptualize the following population of measurements 162, 152, 177, 157, 184, 176, 165, 181, clxx, 163 a. image the mean b. sum up the median Answers a. Meanpic b. Median pic pic 3. The following data represent the number of children in a examine of 10 families from a certain community , 2, 1, 1, 5, 3, 0, 1, 0, 2 a. compute the range b. compute the version c. compute the standard aberrancy Answers a. Range pic b. Variancepic Remember that pic picpicpicpic 14 2. 14. 41 22 0. 10. 01 31-0. 90. 81 41-0. 90. 81 55 3. 19. 61 63 1. 11. 21 70-1. 93. 61 81-0. 90. 81 90-1. 93. 61 102 0. 10. 01 Total1924. 9 pic Method 2pic picpicpic 1416 224 311 411 5525 639 700 811 900 1024 Total1961 pic This is the same answer as we would expect. c. The standard parenthesis is pic 4. Consider the following population of measurements 162, 152, 177, 157, 184, 176, 165, 181, one hundred seventy, 163 a. ompute the standard deviation Answer pic Remember that pic picpicpicpic 1 162 -6. 70 44. 89 2 152 -16. 70 278. 89 3 177 8. 30 68. 89 4 157 -11. 70 136. 89 5 184 15. 30 234. 09 6 176 7. 30 53. 29 7 165 -3. 0 13. 69 8 181 12. 30 151. 29 9 170 1. 30 1. 69 10 163 -5. 70 32. 49 Total 1687. 0 1016. 10 pic The standard deviation is the square root of the segmentation pic Method 2pic picpicpic 1 162 26244 2 152 23104 3 177 31329 4 157 24649 5 184 33856 6 176 30976 7 165 27225 8 181 32761 9 170 28900 10 163 26569 1687 285613 pic As before, the standard deviation is the square root of the variance pic 5. Monthly rent data in dollars for a sample of one-bed get on apartments in a small town in Iowa ar e as follows 220, 216, 220, 205, 210, 240, 195, 235, 204 and 205. a. compute the sample monthly average rent. b. compute the sample median. c. what is the mode? Answers a. Average pic picpic 1 220 2 216 3 220 4 205 5 210 6 240 7 195 8 235 9 204 10 205 2,cl pic b. MEDIAN 195 204 205 205 210 216 220 220 235 240 pic c. MODE205 and 220 (bimodal) 6. A sample of 25 families was asked how many pets they owned. Their responses were summarized in the following table Number of Pets 0 1 2 3 4 5 Number of Families 3 10 5 4 2 1 Determine the mean, median and the mode of the number of pets owned per family. ANSWERS a. MEANpic picpicpicpic 0 3 0 1 10 10 2 5 10 3 4 12 4 2 8 5 1 5 25 45 pic b. MEDIAN1 median is 13th observation. c. MODE 1 or so families have 1 pet. 7.The following data represent the ages in long time of a sample of 25 employees from a government department 31,43,56,23,49,42,33,61,44,28,48,38,44,35,40,64,52,42,47,39,53,27,36,35 and 20. Construct a rela tive frequency distribution for the data, using five class intervals and the nurture 20 as the lower limit of the first class. 20 23 27 28 4 31 33 35 35 36 38 39 7 40 42 42 43 44 44 47 48 49 9 52 53 56 3 61 64 2 Class Limits Frequency comparative Frequency 20 upto 30 4 0. 16 30 upto 40 7 0. 28 40 upto 50 9 0. 36 50 upto 60 3 0. 12 60 upto 70 2 0. 8 25 1. 00 8. How many hours a day do college students spend studying? That question was asked to cytosine college students, and the data are presented in the table below. Hours per DayFrequency 0-225 2-448 4-615 6-89 8-103 a. compute the range b. compute the average hours per day washed-out studying. c. compute the variance of the number of hours per day spent studying d. find the median e. find the mode Answers a. The range is 10-0 = 10 b. Averagepic picpicpicpicpic 1 0-2 25 1 25 2 2-4 48 3 revenue 3 4-6 15 5 75 4 6-8 9 7 63 5 8-10 3 9 27 100 334 pic c. compute the variance of the number of hours per day spent studying pic note that pic picpicpicpicpicpicpic 1 0-2 25 1 -2. 34 5. 4756 136. 89 2 2-4 48 3 -0. 34 0. 1156 5. 488 3 4-6 15 5 1. 66 2. 7556 41. 334 4 6-8 9 7 3. 66 13. 3956 120. 5604 5 8-10 3 9 5. 66 32. 0356 96. 1068 100 53. 7780 400. 4400 pic Method 2 pic picpicpicpicpicpic 1 0-2 25 1 25 25 2 2-4 48 3 144 432 3 4-6 15 5 75 375 4 6-8 9 7 63 441 5 8-10 3 9 27 243 100 334 1516 pic d. mystify the MEDIAN3 e. Find the MODE3 9. The following data is for the daily style grade in $, for staying at various hotels in downtown LA Hotels Offering RateDaily room rate 130 50 1470 690 3110 4130 1150 1170a. Compute the range b. Compute the average daily room rate. c. Compute the variance of the room rate. d. Find the median. e. Find the mode. Answers a. Range 170-30 =one hundred forty b. Averagepicwhere pic picpicpicpic 1 1 30 30 2 7 50 350 3 14 70 980 4 6 90 540 5 3 110 330 6 4 130 520 7 1 150 150 8 1 170 170 37 3070 pic c. Variance of the room rate pic picpicpicpicpicpic 1 1 30 -52. 9730 2806. 1359 2806. 1359 2 7 50 -32. 9730 1087. 2169 7610. 5186 3 14 70 -12. 9730 168. 2980 2356. 1724 4 6 90 7. 0270 49. 3791 296. 747 5 3 110 27. 0270 730. 4602 2191. 3806 6 4 130 47. 0270 2211. 5413 8846. 1651 7 1 150 67. 0270 4492. 6224 4492. 6224 8 1 170 87. 0270 7573. 7034 7573. 7034 37 136. 2162 36172. 9730 picMethod 2 pic picpicpicpicpic 1 1 30 30 900 2 7 50 350 17500 3 14 70 980 68600 4 6 90 540 48600 5 3 110 330 36300 6 4 130 520 67600 7 1 150 150 22500 8 1 170 170 28900 37 3,070 290,900 pic d. Find the MEDIAN70 e. Find the mode70Solutions HmwkISDS-361AExercises 1. Mean, Median, Mode, Range, Variance & SD Panayiotis Skordi 1. A basketball player has the following points for seven games 20, 25, 32, 18, 19, 22, 30 Compute the following measures of central location a. mean b. median c. mode Answers a. Meanpic b. Medianp ic c. Mode There is no mode. 2. Consider the following population of measurements 162, 152, 177, 157, 184, 176, 165, 181, 170, 163 a. compute the mean b. compute the median Answers a. Meanpic b. Median pic pic 3. The following data represent the number of children in a sample of 10 families from a certain community , 2, 1, 1, 5, 3, 0, 1, 0, 2 a. compute the range b. compute the variance c. compute the standard deviation Answers a. Range pic b. Variancepic Remember that pic picpicpicpic 14 2. 14. 41 22 0. 10. 01 31-0. 90. 81 41-0. 90. 81 55 3. 19. 61 63 1. 11. 21 70-1. 93. 61 81-0. 90. 81 90-1. 93. 61 102 0. 10. 01 Total1924. 9 pic Method 2pic picpicpic 1416 224 311 411 5525 639 700 811 900 1024 Total1961 pic This is the same answer as we would expect. c. The standard deviation is pic 4. Consider the following population of measurements 162, 152, 177, 157, 184, 176, 165, 181, 170, 163 a. ompute the standard deviation Answer pic Remember that pic picpicpicpic 1 162 -6. 70 44. 89 2 152 -16. 70 278. 89 3 177 8. 30 68. 89 4 157 -11. 70 136. 89 5 184 15. 30 234. 09 6 176 7. 30 53. 29 7 165 -3. 0 13. 69 8 181 12. 30 151. 29 9 170 1. 30 1. 69 10 163 -5. 70 32. 49 Total 1687. 0 1016. 10 pic The standard deviation is the square root of the variance pic Method 2pic picpicpic 1 162 26244 2 152 23104 3 177 31329 4 157 24649 5 184 33856 6 176 30976 7 165 27225 8 181 32761 9 170 28900 10 163 26569 1687 285613 pic As before, the standard deviation is the square root of the variance pic 5. Monthly rent data in dollars for a sample of one-bedroom apartments in a small town in Iowa are as follows 220, 216, 220, 205, 210, 240, 195, 235, 204 and 205. a. compute the sample monthly average rent. b. compute the sample median. c. what is the mode? Answers a. Average pic picpic 1 220 2 216 3 220 4 205 5 210 6 240 7 195 8 235 9 204 10 205 2,150 pic b. MEDIAN 195 204 205 205 210 216 220 220 235 240 pic c. MODE205 and 220 (bimodal) 6. A sample of 25 families was asked how many pets they owned. Their responses were summarized in the following table Number of Pets 0 1 2 3 4 5 Number of Families 3 10 5 4 2 1 Determine the mean, median and the mode of the number of pets owned per family. ANSWERS a. MEANpic picpicpicpic 0 3 0 1 10 10 2 5 10 3 4 12 4 2 8 5 1 5 25 45 pic b. MEDIAN1 median is 13th observation. c. MODE 1 most families have 1 pet. 7.The following data represent the ages in years of a sample of 25 employees from a government department 31,43,56,23,49,42,33,61,44,28,48,38,44,35,40,64,52,42,47,39,53,27,36,35 and 20. Construct a relative frequency distribution for the data, using five class intervals and the value 20 as the lower limit of the first class. 20 23 27 28 4 31 33 35 35 36 38 39 7 40 42 42 43 44 44 47 48 49 9 52 53 56 3 61 64 2 Class Limits Frequency Relative Frequency 20 upto 30 4 0. 16 30 upto 40 7 0. 28 40 upto 50 9 0. 36 50 upto 60 3 0. 12 60 upto 70 2 0. 8 25 1. 00 8. How many hours a day do college students spend studying? That question was asked to 100 college students, and the data are presented in the table below. Hours per DayFrequency 0-225 2-448 4-615 6-89 8-103 a. compute the range b. compute the average hours per day spent studying. c. compute the variance of the number of hours per day spent studying d. find the median e. find the mode Answers a. The range is 10-0 = 10 b. Averagepic picpicpicpicpic 1 0-2 25 1 25 2 2-4 48 3 144 3 4-6 15 5 75 4 6-8 9 7 63 5 8-10 3 9 27 100 334 pic c. compute the variance of the number of hours per day spent studying pic note that pic picpicpicpicpicpicpic 1 0-2 25 1 -2. 34 5. 4756 136. 89 2 2-4 48 3 -0. 34 0. 1156 5. 488 3 4-6 15 5 1. 66 2. 7556 41. 334 4 6-8 9 7 3. 66 13. 3956 120. 5604 5 8-10 3 9 5. 66 32. 0356 96. 1068 100 53. 7780 400. 4400 pic Method 2 pic picpicpicpicpicpic 1 0-2 25 1 25 25 2 2-4 48 3 144 432 3 4-6 15 5 75 375 4 6-8 9 7 63 441 5 8-10 3 9 27 243 100 334 1516 pic d. Find the MEDIAN3 e. Find the MODE3 9. The following data is for the daily room rate in $, for staying at various hotels in downtown LA Hotels Offering RateDaily room rate 130 50 1470 690 3110 4130 1150 1170a. Compute the range b. Compute the average daily room rate. c. Compute the variance of the room rate. d. Find the median. e. Find the mode. Answers a. Range 170-30 =140 b. Averagepicwhere pic picpicpicpic 1 1 30 30 2 7 50 350 3 14 70 980 4 6 90 540 5 3 110 330 6 4 130 520 7 1 150 150 8 1 170 170 37 3070 pic c. Variance of the room rate pic picpicpicpicpicpic 1 1 30 -52. 9730 2806. 1359 2806. 1359 2 7 50 -32. 9730 1087. 2169 7610. 5186 3 14 70 -12. 9730 168. 2980 2356. 1724 4 6 90 7. 0270 49. 3791 296. 747 5 3 110 27. 0270 730. 4602 2191. 3806 6 4 130 47. 0270 2211. 5413 8846. 1651 7 1 150 67. 0270 4492. 6224 4 492. 6224 8 1 170 87. 0270 7573. 7034 7573. 7034 37 136. 2162 36172. 9730 picMethod 2 pic picpicpicpicpic 1 1 30 30 900 2 7 50 350 17500 3 14 70 980 68600 4 6 90 540 48600 5 3 110 330 36300 6 4 130 520 67600 7 1 150 150 22500 8 1 170 170 28900 37 3,070 290,900 pic d. Find the MEDIAN70 e. Find the mode70