4- Variability
A population of N = 8 scores has a standard deviation of σ = 3. What is the value of SS, the sum of the squared deviations, for this population? a. 72 b. 24 c. 8√3 d. 9/8 = 1.125
a
A set of scores ranges from a high of X = 24 to a low of X = 12 and has a mean of 18. Which of the following is the most likely value for the standard deviation for these scores? a. 3 points b. 6 points c. 12 points d. 24 points
a
All the possible samples of n = 3 scores are selected from a population with μ = 30 and σ = 5 and the mean is computed for each of the samples. If the average is calculated for all of the sample means, what value will be obtained? a. 30 b. Greater than 30 c. Less than 30 d. Near 30 but not exactly equal to 30.
a
Which of the following explains why it is necessary to make a correction to the formula for sample variance? a. If sample variance is computed by dividing by n, instead of n - 1, the resulting values will tend to underestimate the population variance. b. If sample variance is computed by dividing by n, instead of n - 1, the resulting values will tend to overestimate the population variance. c. If sample variance is computed by dividing by n - 1, instead of n, the resulting values will tend to underestimate the population variance. d. If sample variance is computed by dividing by n - 1, instead of n, the resulting values will tend to underestimate the population variance.
a
Which of the following sets of scores has the largest variance? a. 1, 3, 8, 12 b. 12, 13, 14, 15 c. 2, 2, 2, 2 d. 22, 24, 25, 27
a
A research study obtains a mean of 12.7 and a standard deviation of 2.3 for a sample of n = 25 participants. How would the sample mean and standard deviation be reported in a research journal report? a. M = 12.7 and s = 2.3 b. M = 17.7 and SD = 23 c. Mn= 12.7 and s = 2.3 d. Mn =12.7 and SD = .3
b
Under what circumstances is the computational formula preferred over the definitional formula when computing SS, the sum of the squared deviations, for a sample? a. When the sample mean is a whole number b. When the sample mean is not a whole number c. When the sample variance is a whole number d. When the sample variance is not a whole number
b
What is the variance for the following sample of n = 5 scores? Scores: 2,0,8,2,3 a. 81/4 = 20.25 b. 36/4 = 9 c. 36/5 = 7.2 d. √9 = 3
b
Which of the following is a consequence of increasing variability? a. The distance from one score to another tends to increase and a single score tends to provide a more accurate representation of the entire distribution. b. The distance from one score to another tends to increase and a single score tends to provide a less accurate representation of the entire distribution. c. The distance from one score to another tends to decrease and a single score tends to provide a more accurate representation of the entire distribution. d. The distance from one score to another tends to decrease and a single score tends to provide a less accurate representation of the entire distribution.
b
For which of the following distributions would X = 35 be an extreme score? a. μ = 30 and σ =5 b. μ = 30 and σ = 10 c. μ = 25 and σ = 5 d. μ = 25 and σ = 10
c
If 5 points are added to every score in a population with a mean of μ = 45 and a standard deviation of σ = 6, What are the new values for μ and σ? a. μ = 45 and it σ = 6 b. μ = 45 and σ = 11 c. μ = 50 and σ = 6 d. μ = 50 and σ = 11
c
If a normal-shaped population with μ = 40 and σ = 5 is shown in a frequency distribution graph, how would the mean and standard deviation be represented? a. The mean is represented by a vertical line drawn at X = 40 and the standard deviation is represented by a vertical line drawn at X = 45. b. The mean is represented by an arrow under the graph pointing up X = 40 and the standard deviation is represented by a vertical line drawn at X = 45 c. The mean is represented by a vertical line drawn at X = 40 and the standard deviation is represented by a horizontal line drawn from X = 40 to X = 45. d. The mean is represented by an arrow under the graph pointing up X = 40 and the standard deviation is represented by a horizontal line drawn from X = 40 to X = 45
c
What is SS, the sum of the squared deviations, for the following population of N = 5 scores? Scores: 1,9,0,2,3 a. 10 b. 41 c. 50 d. 95
c
What is the range for the following set of scores? Scores: 5, 7, 9, 15 a. 4 points b. 5 points c. 10 or 11 points d. 15 points
c
A researcher takes a sample from a population and computes a statistic for the sample. Which of the following statements is correct? a. If the sample statistic overestimates the corresponding population parameter, then the statistic is biased. b. If the sample statistic underestimates the corresponding population parameter, then the statistic is biased. c. If the sample statistic is equal to the corresponding population parameter, then the statistic is unbiased. d. None of the above
d
A researcher takes all of the possible samples of n = 4 from a population. Next, the researcher computes a statistic for each sample and calculates the average of all the statistics. Which of the following statements is the most accurate? a. If the average statistic overestimates the corresponding population parameter, then the statistic is biased. b. If the average statistic underestimates the corresponding population parameter, then the statistic is biased. c. If the average statistic is equal to the corresponding population parameter, then the statistic is unbiased. d. All of the above.
d
For the following scores, which of the following actions will increase the range? Scores: 3, 7, 10, 15 a. Add 4 points to the score X = 3 b. Add 4 points to the score X - 7 c. Add 4 points to the score X = 10 d. Add 4 points to the score X = 15
d
What is the standard deviation for the following population of scores? Scores: 1,3,9,3 a. 36 b. 9 c. 6 d. 3
d
What is the variance for the following set of scores? Scores: 4, 1, 7 a. 66/3 = 22 b. 18 c. 9 d. 6
d
