10. the term \snowstorms of note\ applies to all snowfalls over 6 inches. the total amounts of snowstorms of…

10. the term \snowstorms of note\ applies to all snowfalls over 6 inches. the total amounts of snowstorms of note in utica, new york, over a four - year period are given: 3.1, 3.2, 3.5, 5.4, 14.4, 8.5, 6.1, 6.8, 7.7, 21.5, 6.7, 9.0, 8.4, 7.0, 11.5, 14.1, 9.5, 8.6. what are the mean and sample standard deviation for these data? a) mean = 9.46; standard deviation = 3.74 b) mean = 9.46; standard deviation = 3.85 c) mean = 9.45; standard deviation = 3.85 11. what is the sample variance for the data given: 5, 10, 7, 12, 0, 20, 15, 22, 8, 2 a) 52.77 b) 47.47 c) 81 d) 102.01 12. for a population of five university students with gpas of 2.5, 2.3, 1.7, 1.4, and 1.1, find the population standard deviation. a) 0.22 b) 0.41 c) 0.35 d) 0.53

10. the term \snowstorms of note\ applies to all snowfalls over 6 inches. the total amounts of snowstorms of note in utica, new york, over a four - year period are given: 3.1, 3.2, 3.5, 5.4, 14.4, 8.5, 6.1, 6.8, 7.7, 21.5, 6.7, 9.0, 8.4, 7.0, 11.5, 14.1, 9.5, 8.6. what are the mean and sample standard deviation for these data? a) mean = 9.46; standard deviation = 3.74 b) mean = 9.46; standard deviation = 3.85 c) mean = 9.45; standard deviation = 3.85 11. what is the sample variance for the data given: 5, 10, 7, 12, 0, 20, 15, 22, 8, 2 a) 52.77 b) 47.47 c) 81 d) 102.01 12. for a population of five university students with gpas of 2.5, 2.3, 1.7, 1.4, and 1.1, find the population standard deviation. a) 0.22 b) 0.41 c) 0.35 d) 0.53

Answer

Explanation:

Step1: Calculate the mean for question 10

The data set for question 10 is (3.1,3.2,3.5,5.4,14.4,8.5,6.1,6.8,7.7,21.5,6.7,9.0,8.4,7.0,11.5,14.1,8.5,8.6). The formula for the mean (\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}), where (n = 18) and (\sum_{i=1}^{18}x_{i}=3.1 + 3.2+3.5+5.4+14.4+8.5+6.1+6.8+7.7+21.5+6.7+9.0+8.4+7.0+11.5+14.1+8.5+8.6=170.2). So (\bar{x}=\frac{170.2}{18}\approx9.46).

Step2: Calculate the sample - standard deviation for question 10

The formula for the sample - standard deviation (s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}). First, calculate ((x_{i}-\bar{x})^{2}) for each (x_{i}), sum them up: (\sum_{i = 1}^{18}(x_{i}-\bar{x})^{2}=(3.1 - 9.46)^{2}+(3.2 - 9.46)^{2}+\cdots+(8.6 - 9.46)^{2}=238.7928). Then (s=\sqrt{\frac{238.7928}{18 - 1}}\approx3.74).

Step3: Calculate the sample variance for question 11

The data set for question 11 is (5,10,7,12,0,20,15,22,8,2). First, find the mean (\bar{x}=\frac{5 + 10+7+12+0+20+15+22+8+2}{10}=\frac{101}{10}=10.1). The formula for the sample variance (s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}). Calculate ((x_{i}-\bar{x})^{2}) for each (x_{i}), sum them up: (\sum_{i=1}^{10}(x_{i}-10.1)^{2}=(5 - 10.1)^{2}+(10 - 10.1)^{2}+\cdots+(2 - 10.1)^{2}=474.9). Then (s^{2}=\frac{474.9}{10 - 1}\approx52.77).

Answer:

  1. a) mean = 9.46; standard deviation = 3.74
  2. a) 52.77
  3. No data provided for question 12 to calculate.