Question

In Problems 5-10, by hand, find the population variance and standard deviation or the sample variance and standard deviation. as indicated. 5. Sample: 20,13,4,8,10 6. Sample: 83,65,91,87,84 7. Population: 3,6,10,12,14 8. Population: 1,19,25,15,12,16,28,13,6 9. Sample: 6,52,13,49,35,25,31,29,31,29 10. Population: 4,10,12,12,13,21 11. Miles per Gallon The following data represent the miles per gallon for a 2013 Ford Fusion for six randomly selected vehicles. Compute the range, sample variance, and sample standard deviation miles per gallon. Source: www.fueleconomy.gov 34.0,33.2,37.0,29.4,23.6,25.9 12. Exam Time The following data represent the amount of time (in minutes) a random sample of eight students took to complete the online portion of an exam in Sullivan's Statistics course. Compute the range, sample variance, and sample standard deviation time. 60.5,128.0,84.6,122.3,78.9,94.7,85.9,89.9 NW 13. Concrete Mix A certain type of concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The strength of concrete is measured by pouring the mix into casting cylinders after it is allowed to set up for 28 days. The following data represent the strength of nine randomly selected casts. Compute the range and sample standard deviation for the strength of the concrete (in psi). 3960,4090,3200,3100,2940,3830,4090,4040,3780 14. Flight Time The following data represent the flight time (in minutes) of a random sample of seven flights from Las Vegas, Nevada, to Newark, New Jersey, on United Airlines. Compute the range and sample standard deviation of flight time. 282,270,260,266,257,260,267

Answer 1

For problem 5, the sample data is [20, 13, 4, 8, 10]. The variance for this can be calculated using formula σ² = Σ (Xi - μ)²/n-1 where Xi represents each score, μ is the mean of the scores, and n is the number of scores. For this data, the variance is 36.0 and the standard deviation (the square root of variance) is 6.0.

In problem 6, the sample data is [83, 65, 91, 87, 84]. Again, using the variance formula, we find the variance to be 100.0 and the standard deviation to be 10.0.

In problem 7, the population data is [3, 6, 10, 12, 14]. The process is the same as before, but when calculating variance for a population, we use n instead of n-1. In this case, the variance is 20.0 and the standard deviation is approximately 4.47.

In problem 8, for the data set [1, 19, 25, 15, 12, 16, 28, 13, 6], the variance is 72.0 and the standard deviation is approximately 8.49.

In problem 9, with the sample data as [6, 52, 13, 49, 35, 25, 31, 29, 31, 29], the variance comes to be 196.0 and the standard deviation is 14.0.

In problem 10, for population data [4, 10, 12, 12, 13, 21], the variance is 30.0 and the standard deviation is approximately 5.48.

Given the miles per gallon for a 2013 Ford Fusion in problem 11 with data [34.0, 33.2, 37.0, 29.4, 23.6, 25.9], the variance is approximately 26.35 and the standard deviation is approximately 5.13.

In problem 12, the sample timing data for the exam [60.5, 128.0, 84.6, 122.3, 78.9, 94.7, 85.9, 89.9] yields a variance of approximately 495.99 and a standard deviation of approximately 22.27.

For problem 13, the strength measures of concrete mix [3960, 4090, 3200, 3100, 2940, 3830, 4090, 4040, 3780] give a variance of 211275.0 and a standard deviation of approximately 459.65.

Finally, for the flight times in problem 14 with data [282, 270, 260, 266, 257, 260, 267], the variance is 71.0 and the standard deviation is approximately 8.43.