Variance, Standard Deviation, and Z-Scores Answers

1. What is the value of SS for the following set of scores? Scores: 0, 1, 4, 5 a. 17 2. A population has SS = 100 and s2 = 4. What is the value of ∑(X – m) for the population? a. 0 3. Which set of scores has the smallest standard deviation? a. 145, 143, 145, 147 4. For a population with µ = 100 and s = 20, what is the X value corresponding to z = –0.75? a. 85 5. Which of the following symbols identifies the sample variance? a. s^2 6. In a population with s = 4, a score of X = 48 corresponds to z = 1.50. The mean for this population is µ = 42. a. True 7. For a population of scores, the sum of the deviation scores is equal to N. a. False 8. What is the variance for the following population of scores? Scores: 5, 2, 5, 4 a. 1.5 9. The sum of the squared deviation scores is SS = 20 for a population of N = 5 scores. What is the variance for this population? a. 4 10. A population with SS = 90 and a variance of 9 has N = 10 scores. a. True 11. A sample of n = 25 scores has M = 20 and s2 = 9. What is the sample standard deviation? a. 3 12. For a population with a standard deviation of s = 6, what is the z-score corresponding to a score that is 12 points above the mean? a. z= 2 13. A sample of n = 20 scores has a mean of M = 45 and a standard deviation of s = 8. In this sample, what is the z-score corresponding to X = 57? a. z= 1.50 14. For a population with µ = 80 and s = 6, what is the z-score corresponding to X = 68? a. -2 15. To calculate the variance for a population, SS is divided by N. a. True 16. What position in the distribution corresponds to a z-score of z = +2.00? a. Above the mean by a distance equal to 2 standard deviations. 17. A score with a value less than or equal to the mean will have a z-score that is less than or equal to zero. a. True 18. After a researcher multiplies every score in a sample by 2, the standard deviation is found to be s = 10. The original sample had a standard deviation of s = 5. a. True 19. A sample consists of n = 16 scores. How many of the scores are used to calculate the range? a. 2 20. Multiplying every score in a sample by 3 will not change the value of the standard deviation. a. False