Determine whether each statement is true or false. If the statement is false, write true one. Sample data set: 17, 15, 23, 7, 9, 13 a) Sample Mean is 14. b) Sample Variance is 83/3. c) Sample Standard Deviation is $\sqrt{33.2}$.
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The sample data set is {17, 15, 23, 7, 9, 13}. The sum of the data is $17 + 15 + 23 + 7 + 9 + 13 = 84$. The number of data points is 6. The sample mean is $\frac{84}{6} = 14$. Therefore, statement a) is true. Show more…
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2.) Determine whether the statements below are true or false. If you answer false, explain why the statement is not true. a.) All of the data values in a data set are the same. The standard deviation of this data set is 0. True b.) The standard deviation is always positive. True c.) If the standard deviation of a data set is 4, then the variance of the data set is 16. d.) If the variance of a data set is 16, then the standard deviation is 4. e.) If the standard deviation of a data set is 9, then the variance is 3.
Adi S.
16. The following data represent a sample of 10 scores on a 20-point statistics quiz: 16, 16, 16, 16, 16, 18, 18, 20, 20, and 20. After the mean, median, range and variance were calculated for the scores, it was discovered that one of the scores of 20 should have been an 18. Which of the following will change when the calculations are redone using the correct scores? a. mean and range b. median and range c. mean and variance d. range and variance e. mean, range, median and variance 17. Which of the following statements is true? a. The sum of the deviations from the mean is always zero. b. The sum of the squared deviations from the mean is always zero. c. The standard deviation is always smaller than the variance. d. The distance between the first and third quartiles is twice the distance between the first and second quartiles. e. None of these is true. 18. A sample of 25 observations has a standard deviation of 4. The sum of the squared deviations from the sample mean is: a. 21 b. 25 c. 100 d. 384 e. 400 19. Which of the following statements is true? a. The population mean will always be larger than the mean of a sample selected from that population. b. The population mean will always be larger than the population median. c. The population mean and the mean of a sample selected from that population will usually be different values. d. The population mean will always be equal to the population median. e. All of these. 20. From a sample of size 100, the following descriptive measures were calculated: median = 23, mean = 20, standard deviation = 5, range = 35; seventy-five sample values are between 10 and 30; and ninety-nine sample values are between 5 and 35. If you knew the sample mean, median, and standard deviation were correct, which one of the following conclusions might you draw? a. The distribution is skewed to the right because the median exceeds the mean. b. The range must have been calculated incorrectly because it should not be seven times the standard deviation's value. c. The number of sample values between 10 and 30 was miscounted. d. The number of sample values between 5 and 35 must have been miscounted because all 100 values must be in this interval. e. All of these.
Madhur L.
The sum of deviations about the arithmetic mean is always equal to zero. A. True B. False 2. The average of the squared deviations about the arithmetic mean is called the variance. A. True B. False 3. The sample standard deviation is calculated by taking the square root of the population standard deviation. A. True B. False 4. The variance of a sample of 81 observations equals 64. The standard deviation of the sample equals a. 9. b. 4096. c. 8. d. 6561.
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