Question 1

The sum of the squared differences of each score from the mean of a distribution divided by the number of scores is the definition for the.

Accepted Answer

The definition provided describes the calculation of sample variance, where the squared differences of each score from the mean are summed up and then divided by the number of scores in the sample.

Question 2

Which of the following sets of scores has the largest estimated population variance?

Accepted Answer

To calculate the estimated population variance, we first find the mean of each set of scores:
A) Mean = 3
B) Mean = 3
C) Mean = 3
D) Mean = 3

Then, we find the deviation of each score from the mean, square each deviation, sum them up, and divide by the sample size minus 1 to get the estimated population variance:
A) (0^2 + 0^2 + 0^2 + 0^2 + 0^2)/4 = 0
B) (1^2 + 0^2 + 1^2 + 1^2 + 4^2)/4 = 1.75
C) (1^2 + 1^2 + 0^2 + 1^2 + 1^2)/4 = 0.75
D) (4^2 + 4^2 + 0^2 + 4^2 + 4^2)/4 = 8

Therefore, set D has the largest estimated population variance of 8.

Question 3

The sample variance is defined as the sum of the.

Accepted Answer

A

Question 4

The range for the scores 10, 11, 12, 14, 16, 16, 16, 18, 19, 20 is.

Accepted Answer

The range is calculated by subtracting the smallest score from the largest score: 20 - 10 = 10.

Question 5

The estimated population variance is defined as the sum of the.

Accepted Answer

The formula for the estimated population variance is the sum of the squared differences of each score from the mean of a distribution divided by the sample size minus 1. This is known as the Bessel's correction and is used to provide an unbiased estimate of the population variance based on a sample. Therefore, the correct choice is C.

Question 6

The numerator in the formula for calculating a variance is called a.

Accepted Answer

The numerator in the formula for calculating a variance is the sum of squares, which is obtained by summing the squared deviations of each score from the mean.

Question 7

Which of the following is the formula for the estimated population variance?

Accepted Answer

The formula for estimated population variance is the sum of the squared differences between each observation and the sample mean, divided by the degrees of freedom (N-1). This is represented by formula D, $\frac{\sum(X-\bar{X})^{2}}{N-1}$. Option A and C only consider the sum of the differences and do not square them, which leads to an incorrect estimate of variance. Option B takes the sum of squared differences but divides it by N rather than N-1, which leads to an underestimate of the population variance.

Question 8

The scores cluster around a measure of central tendency in a distribution, the that measure of central tendency represents the scores.

Accepted Answer

The statement is saying that when scores cluster around a measure of central tendency in a distribution, the higher the degree of clustering, the better that measure of central tendency represents the scores. Therefore, more clustering (of scores) leads to better representation by the measure of central tendency.

Question 9

The range is the.

Accepted Answer

The range is defined as the difference between the highest and the lowest score in a distribution. This is a commonly used descriptive statistic to summarize the variability in a set of scores.

Question 10

Which of the following sets of scores has the largest range?

Accepted Answer

The range is the difference between the highest and lowest scores in a set. Set A has a range of 6 (7-1), while the other sets have ranges of 4 (B), 2 (C), and 0 (D). Therefore, set A has the largest range.

Question 11

The sum of the squared deviations from a population mean divided by the population size is the definition for the.

Accepted Answer

The formula given in the question is the definition for population variance.

Question 12

The term refers to how much scores in a distribution differ from each other.

Accepted Answer

Variability refers to how much scores in a distribution differ from each other. It is a measure of the spread or dispersion of the distribution. Modality refers to the number of peaks or modes in a distribution, stability refers to the consistency of scores over time, and similarity refers to the degree to which scores are alike or resemble each other.

Question 13

Which of the following is the formula for the variance of a sample used to estimate the population variance?

Accepted Answer

The formula for the variance of a sample used to estimate the population variance is given by Option D, which is $\frac { \sum ( X - \bar { X } ) ^ { 2 } } { N - 1 }$. This is because the denominator in the formula is N - 1, as the sample variance is estimated using the sample mean instead of the population mean. Option A is incorrect because it does not include the squared deviations, and Option B is incorrect because it uses N instead of N-1 as the denominator. Option C is the formula for the sample variance, not the variance of the sample used to estimate the population variance.

Question 14

The dispersion there is among scores in a distribution, the the mean depicts a typical score for that distribution.

Accepted Answer

When there is more dispersion (variation) among scores in a distribution, the mean may be less reliable as a representation of the typical score for that distribution. This is because extreme scores can pull the mean in a direction that is not representative of the majority of scores. Therefore, when there is more dispersion, the mean may be less useful.

Question 15

Which of the following is the formula for the population variance?

Accepted Answer

The formula for population variance is the sum of the squared differences between each data point and the population mean, divided by the total number of data points. This can be written as $\frac { \sum ( X - \mu ) ^ { 2 } } { N _ { \text {population } } }$, which is option D. Options A and C are not correct because they do not include the squaring step. Option B is the formula for sample variance, which uses a slightly different denominator (n-1) to estimate the true population variance.

Question 16

The sum of the squared deviations from the mean divided by the number of scores minus one is the definition for the.

Accepted Answer

The answer of The sum of the squared deviations from...

Question 17

The estimated population variance is represented by.

Accepted Answer

The estimated population variance is typically represented by s squared, which is denoted as s². This is because the sample variance is an estimate of the population variance, and we use the notation s² to represent the sample variance. The population variance is denoted by σ², but since we don't usually know the actual population variance, we use the sample variance as an estimate. Therefore, the best choice is B.

Question 18

The population variance is represented by.

Accepted Answer

The population variance is typically denoted by the symbol $\sigma ^ {2}$. Option A ($S^{2}$) is used to represent the sample variance, while option B ($s^{2}$) is also used to represent the sample variance, but in a different notation. Option C ($\sigma$) is the symbol commonly used to represent the population standard deviation. Therefore, the best choice for population variance is option D ($\sigma ^ {2}$).

Question 19

A measure of central tendency of a distribution is most representative of individual scores when there is variability among the scores.

Accepted Answer

When there is little variability among scores, a measure of central tendency, like the mean, is most representative of individual scores because the scores are more similar and clustered around the central value.

Question 20

The population variance is defined as the sum of the.

Accepted Answer

The population variance is defined as the squared differences of each score from the mean of a population divided by the population size. This is the formula for population variance:

σ² = Σ(x-μ)²/N

where σ² is the variance, Σ is the sum, x is each individual score in the population, μ is the population mean, and N is the number of scores in the population.

Quiz 5: Looking at Data: Measures of Variability