Question 1

If the highest score in a distribution is X = 16 and the lowest is X = 4,then the range is 12 or 13 points.

Accepted Answer

The range is calculated by subtracting the lowest score from the highest score. In this case, 16 - 4 = 12, so the range is 12 points. However, it is possible that there may be a score of 5 or 6, which would make the range 13 points. Therefore, both 12 and 13 points are possible, making option A true.

Question 2

The range is usually considered to be a relatively crude measure of variability.

Accepted Answer

The range only considers the difference between the maximum and minimum values and does not take into account the distribution of the data. Other measures of variability, such as variance or standard deviation, provide more detailed information about the spread of data.

Question 3

A positive deviation always indicates a score that is less than the mean.

Accepted Answer

A positive deviation indicates a score that is greater than the mean.

Question 4

Which of the following actions will have no effect on the value of the standard deviation?
A)Multiply each score in the distribution by 2
B)Divide each score in the distribution by 2
C)Subtract 5 points from every score in the distribution
D)All of the other actions will change the value of the standard deviation

Accepted Answer

Subtracting or adding a constant to every score in a distribution shifts the entire distribution without affecting the spread or dispersion of the scores, which is what standard deviation measures. Multiplying or dividing each score by a constant (other than 1) changes the spread of the distribution, thus affecting the standard deviation.

Question 5

For a population of scores,the sum of the deviation scores is equal to N.

Accepted Answer

For a population of scores, the sum of the deviation scores (where deviation is defined as each score minus the mean) is always equal to 0, not N. This is because the mean is the average value, and deviations above and below the mean cancel each other out.

Question 6

For a population with µ = 60,which of the following values for the population standard deviation would cause X = 68 to have the most extreme position in the distribution?
A)σ = 1
B)σ = 2
C)σ = 3
D)σ = 4

Accepted Answer

A smaller standard deviation (σ = 1) means that the scores are more closely clustered around the mean (µ = 60). Therefore, a score of X = 68 would be more extreme or further away from the mean in terms of standard deviation units when the standard deviation is smallest.

Question 7

One sample is selected to represent scores in treatment 1 and a second sample is used to represent scores in treatment 2.Which set of sample statistics would present the clearest picture of a real difference between the two treatments?
A)M1 = 36, M2 = 40, and both variances = 43
B)M1 = 36, M2 = 40, and both variances = 6
C)M1 = 38, M2 = 40, and both variances = 43
D)M1 = 38, M2 = 40, and both variances = 6

Accepted Answer

Lower variances indicate that the data points are closer to the mean, making the difference between the means (M1 = 36, M2 = 40) more pronounced and clearer to interpret as a real difference between the two treatments.

Question 8

On an exam with a mean of μ = 70,you have a score of X = 75.Which of the following values for the standard deviation would give you the highest position within the class?
A)σ = 1
B)σ = 5
C)σ = 10
D)Cannot determine from the information given

Accepted Answer

A smaller standard deviation (σ = 1) means that most scores are closer to the mean, so a score of 75 would be farther from the mean in terms of standard deviations, placing you higher within the class distribution.

Question 9

On an exam with a mean of μ = 70,you have a score of X = 65.Which of the following values for the standard deviation would give you the highest position within the class?
A)σ = 1
B)σ = 5
C)σ = 10
D)Cannot determine from the information given

Accepted Answer

A larger standard deviation means that scores are more spread out. With a score of 65, a larger standard deviation (σ = 10) would place you closer to the mean relative to others, giving you a higher position in the class.

Question 10

A population of scores has µ = 50 and σ = 5.If every score in the population is multiplied by 3,then what are the new values for the mean and standard deviation?
A)µ = 50 and σ = 5
B)µ = 50 and σ = 15
C)µ = 150 and σ = 5
D)µ = 150 and σ = 15

Accepted Answer

When every score in a population is multiplied by a constant, the mean (µ) is also multiplied by that constant, and the standard deviation (σ) is multiplied by the absolute value of that constant. Therefore, the new mean is 3*50 = 150, and the new standard deviation is 3*5 = 15.

Question 11

For a population of N = 4 scores with ΣX = 10 and ΣX² = 30,SS = 5.

Accepted Answer

To compute SS, we can use the formula:
SS = ΣX² - (ΣX)²/N
Plugging in the given values, we get:
SS = 30 - (10)²/4
SS = 30 - 25
SS = 5
So the given value of SS is true.

Question 12

A population has µ = 50 and σ = 5.If 10 points are added to every score in the population,what are the new values for the mean and standard deviation?
A)µ = 50 and σ = 5
B)µ = 50 and σ = 15
C)µ = 60 and σ = 5
D)µ = 60 and σ = 15

Accepted Answer

Adding a constant value to every score in a population will not change the standard deviation of the population, but it will change the mean by the same amount added. 
So the new mean will be 50+10=60 and the standard deviation will still be 5. Therefore, the correct answer is C.

Question 13

For a population,a deviation score is computed as X - μ.

Accepted Answer

This is true. A deviation score is calculated by subtracting the population mean (μ) from the individual data point (X).

Question 14

There is a 6-point difference between two sample means.If the two samples have the same variance,which of the following values would make the mean difference easiest to see in a graph showing the two distributions? A)s² = 2 B)s² = 8 C)s² = 16 D)s² = 64

Accepted Answer

When the variance (s2) is smaller (in this case, s2 = 2), the distributions are tighter, making the difference between the two means easier to see visually on a graph.

Question 15

The range and the standard deviation are both measures of distance.

Accepted Answer

Both range and standard deviation quantify the amount of variability or dispersion within a set of data, and they both involve measuring distance from the mean or central point. The range represents the distance between the maximum and minimum values in a dataset, while the standard deviation measures the average distance of each data point from the mean.

Question 16

Under what circumstances would a score that is 10 points below the mean be considered an extreme value?
A)When the mean is much greater than 10
B)When the mean is much less than 10
C)When the standard deviation is much greater than 10
D)When the standard deviation is much less than 10

Accepted Answer

An extreme value is one that deviates significantly from the usual or expected values. If the score is 10 points below the mean but the standard deviation is also large, then this deviation may not be considered extreme. However, if the standard deviation is small and the score is 10 points below the mean, then this deviation is significant and may be considered extreme. Therefore, option D is the best choice as it specifies the importance of the standard deviation in determining extreme scores.

Question 17

A population with SS = 90 and a variance of 9 has N = 10 scores.

Accepted Answer

The variance is calculated as SS (Sum of Squares) divided by N (Number of scores), so if SS = 90 and N = 10, then variance = 90 / 10 = 9.

Question 18

The value for SS can never be less than zero.

Accepted Answer

The sum of squares (SS) is always a non-negative value, as it involves squaring the differences between the observed values and their mean. Consequently, it is impossible for the SS value to be negative.

Question 19

To calculate the variance for a population,SS is divided by N.

Accepted Answer

To calculate the variance for a population, SS (sum of squared deviations from the mean) is divided by N (total number of observations in the population). This gives the average squared deviation of individual scores from the population mean.

Question 20

Which of the following is true for most distributions?
A)Around 30% of the scores will be located within one standard deviation of the mean.
B)Around 50% of the scores will be located within one standard deviation of the mean.
C)Around 70% of the scores will be located within one standard deviation of the mean.
D)Around 90% of the scores will be located within one standard deviation of the mean.

Accepted Answer

This is known as the empirical rule or the 68-95-99.7 rule, which states that for a normally distributed dataset, approximately 68% of the scores will fall within one standard deviation of the mean. This is true for most distributions.

Quiz 4: Variability.

If the highest score in a distribution is X = 16 and the lowest is X = 4,then the range is 12 or 13 points.

The range is usually considered to be a relatively crude measure of variability.

A positive deviation always indicates a score that is less than the mean.

Which of the following actions will have no effect on the value of the standard deviation?

For a population of scores,the sum of the deviation scores is equal to N.

For a population with µ = 60,which of the following values for the population standard deviation would cause X = 68 to have the most extreme position in the distribution?

One sample is selected to represent scores in treatment 1 and a second sample is used to represent scores in treatment 2.Which set of sample statistics would present the clearest picture of a real difference between the two treatments?

On an exam with a mean of μ = 70,you have a score of X = 75.Which of the following values for the standard deviation would give you the highest position within the class?

On an exam with a mean of μ = 70,you have a score of X = 65.Which of the following values for the standard deviation would give you the highest position within the class?

A population of scores has µ = 50 and σ = 5.If every score in the population is multiplied by 3,then what are the new values for the mean and standard deviation?

For a population of N = 4 scores with ΣX = 10 and ΣX² = 30,SS = 5.

A population has µ = 50 and σ = 5.If 10 points are added to every score in the population,what are the new values for the mean and standard deviation?

For a population,a deviation score is computed as X - μ.

There is a 6-point difference between two sample means.If the two samples have the same variance,which of the following values would make the mean difference easiest to see in a graph showing the two distributions?

The range and the standard deviation are both measures of distance.

Under what circumstances would a score that is 10 points below the mean be considered an extreme value?

A population with SS = 90 and a variance of 9 has N = 10 scores.

The value for SS can never be less than zero.

To calculate the variance for a population,SS is divided by N.

Which of the following is true for most distributions?