Question 1

If the variance for a sample is computed and it is found to be rather large,the numbers

Accepted Answer

A large variance indicates that the data points in the sample are spread out around the mean. Therefore, option C is the correct choice. The other options (A, B, and D) all suggest that the data points in the sample are closely clustered together, which would result in a small variance.

Question 2

The variance can never be

Accepted Answer

The variance is a measure of the spread of numbers in a dataset and is calculated as the average of the squared differences from the Mean. Since it involves squaring differences, it cannot be negative.

Question 3

A group of 10 students participated in a study of nutritional awareness.What is the sample standard deviation  of their scores? Their scores follow: 20,19,22,20,15,18,15,21,19,20

Accepted Answer

The answer of A group of 10 students participated in...

Question 4

In a positively skewed distribution,the estimated population variance  will be _____ than the estimated population standard deviation  .In a negatively skewed distribution the estimated population variance  will be _____ than the estimated population standard deviation  .

Accepted Answer

The answer of In a positively skewed distribution,the estimated population...

Question 5

and  are considered biased estimates for the population standard deviation and variance because,over many calculations,they tend to be

Accepted Answer

The answer of  and  are considered biased estimates...

Question 6

In general,the larger the value of the standard deviation,

Accepted Answer

Standard deviation measures the spread of data. A larger standard deviation indicates that the data points are more spread out from the mean, resulting in a wider distribution.

Question 7

The standard deviation,  ,is a measure of how far scores deviate from

Accepted Answer

The standard deviation is a measure of how far scores deviate from the mean. This makes it a measure of the variability or spread of the data around the average score. The other options (median, mode) do not take into account the entire distribution of scores and are only measures of central tendency.

Question 8

If we add to and subtract from ,the interval we have created

Accepted Answer

The answer of If we add  to  <sub>...

Question 9

Suppose we compute  and find that it is equal to 5.5.How do we interpret this number?

Accepted Answer

The value 5.5 is the sample standard deviation, which is a measure of how much the numbers in the sample deviate from the mean. Therefore, we can interpret this number as saying that, on average, the numbers in the sample deviate 5.5 units from the mean.

Question 10

In roughly normal distributions,the standard deviation is approximately

Accepted Answer

The standard deviation in a roughly normal distribution is approximately one-sixth of the range. This is because the range (difference between the maximum and minimum values) encompasses about 99.7% of the data (assuming the data follows a normal distribution), which is roughly 6 standard deviations (3 standard deviations on either side of the mean).

Question 11

If the sample standard deviation  for a set of data with N = 6 is found to be 3.17,then what is the sample variance  ?

Accepted Answer

The answer of If the sample standard deviation  for...

Question 12

The standard deviation is always

Accepted Answer

The standard deviation is the square root of the variance. Therefore, option D is correct. The formula for variance is (sum of the squared deviations from the mean)/n, and the formula for the standard deviation is the square root of the variance. Since the variance involves squared units, taking the square root gives us the standard deviation in the original units of measurement.

Question 13

Sample standard deviation is defined as the square root of the

Accepted Answer

The definition of sample standard deviation involves taking the square root of the average of the squared deviations around the mean. This is because the squared deviations ensure that negative and positive deviations do not cancel each other out, and taking the average ensures that the measure is representative of the variability of the data. Therefore, the correct choice is B.

Question 14

Unbiased estimators  and  of the population parameters will produce values that are _____ those produced by the biased estimators  and  .

Accepted Answer

The answer of Unbiased estimators  and  of the...

Question 15

If the sample standard deviation  for a set of data with N = 6 is found to be 3.17,then what would be the estimated population standard deviation  ?

Accepted Answer

When calculating the estimated population standard deviation, we would use the sample standard deviation formula: 
s = sqrt((Σ(x - x̄)^2) / (n - 1))
where s is the sample standard deviation, x̄ is the sample mean, and n is the sample size.

To estimate the population standard deviation, we would use the formula:
σ = s / sqrt(n)
where σ is the population standard deviation.

Substituting s = 3.17 and n = 6, we get:
σ = 3.17 / sqrt(6) = 1.29

Therefore, the estimated population standard deviation would be 1.29. However, this is not one of the answer choices. We need to round our answer to the nearest hundredth to match one of the answer choices. 
Rounding 1.29 to the nearest hundredth gives us 1.30. 
Of the answer choices, the one closest to 1.30 is A) 3.47, which is approximately 2.67 times larger than our estimated population standard deviation.

Question 16

If a sample has a small standard deviation,we can say that the scores in the sample are

Accepted Answer

A small standard deviation indicates that the scores in the sample are consistent and clustered closely around the mean. This means there is less variability in the data and the scores are more predictable.

Question 17

and  are considered biased estimates for the population standard deviation and variance because

Accepted Answer

The answer of  and  are considered biased estimates...

Question 18

Multiplying each of the scores in a distribution by a constant

Accepted Answer

When you multiply each score in a distribution by a constant, the standard deviation of the distribution is also multiplied by the absolute value of that constant. This is because standard deviation is a measure of dispersion that changes in scale with the data.

Question 19

A psychology professor wanted to describe his/her class in terms of the personality characteristic of introversion/extroversion.The population variance was estimated to be 2.56.What does this mean?

Accepted Answer

The population variance being estimated as 2.56 indicates the amount of variability in the scores of the class with respect to introversion/extroversion. It does not provide information about the accuracy of the prediction of individual scores based on the population mean. However, as population variance is a measure of dispersion or spread of the scores, the professor can expect to be in error by about 2.56 when predicting individual scores based on the population mean. Therefore, option A is the best choice.

Question 20

Adding a constant to or subtracting a constant from each of the scores in a distribution

Accepted Answer

Adding or subtracting a constant from each of the scores in a distribution does not affect the spread of the data, which is quantified by the standard deviation. As a result, the value of the standard deviation remains the same.

Quiz 5: Measures of Variability: Range, variance, and Standard Deviation

If the variance for a sample is computed and it is found to be rather large,the numbers

The variance can never be

A group of 10 students participated in a study of nutritional awareness.What is the sample standard deviation of their scores? Their scores follow: 20,19,22,20,15,18,15,21,19,20

In a positively skewed distribution,the estimated population variance will be _ than the estimated population standard deviation .In a negatively skewed distribution the estimated population variance will be _ than the estimated population standard deviation .

and are considered biased estimates for the population standard deviation and variance because,over many calculations,they tend to be

In general,the larger the value of the standard deviation,

The standard deviation, ,is a measure of how far scores deviate from

If we add to and subtract from ,the interval we have created

Suppose we compute and find that it is equal to 5.5.How do we interpret this number?

In roughly normal distributions,the standard deviation is approximately

If the sample standard deviation for a set of data with N = 6 is found to be 3.17,then what is the sample variance ?

The standard deviation is always

Sample standard deviation is defined as the square root of the

Unbiased estimators and of the population parameters will produce values that are _____ those produced by the biased estimators and .

If the sample standard deviation for a set of data with N = 6 is found to be 3.17,then what would be the estimated population standard deviation ?

If a sample has a small standard deviation,we can say that the scores in the sample are

and are considered biased estimates for the population standard deviation and variance because

Multiplying each of the scores in a distribution by a constant

A psychology professor wanted to describe his/her class in terms of the personality characteristic of introversion/extroversion.The population variance was estimated to be 2.56.What does this mean?

Adding a constant to or subtracting a constant from each of the scores in a distribution