Question 1

In the formula for computing the standard deviation, what does the Greek letter "?" represent?

Accepted Answer

The Greek letter "?" (sigma) represents summation in the formula for computing the standard deviation, indicating the sum of all the values.

Question 2

What will the sum of the deviations from the mean always equal?

Accepted Answer

The sum of the deviations from the mean will always equal 0, as some deviations above the mean cancel out with deviations below the mean.

Question 3

Which of the following is the correct function for calculating an unbiased estimate of the variance in the population?

Accepted Answer

D

Question 4

In the formula for computing the variance, what does the letter "n" represent?

Accepted Answer

The letter "n" represents the sample size, which is the number of individuals or cases in the group. The formula for variance is calculated by subtracting the mean from each individual score, squaring the differences, summing them up, and dividing by the sample size minus one. Therefore, "n" plays a crucial role in determining the accuracy of the variance calculation.

Question 5

When subtracting the largest number in a distribution from the smallest, what type of variability is being calculated?

Accepted Answer

The range is the difference between the largest and smallest values in a distribution. Therefore, when subtracting the largest number from the smallest, we are calculating the range which represents the variability in the data.

Question 6

What is the most general measure of variability?

Accepted Answer

The range is the simplest and most general measure of variability. It is the difference between the largest and smallest values in the data set, and provides a quick indicator of how widely spread out the data is.

Question 7

Which of the following sets of scores has the most variability?

Accepted Answer

The set of scores in option A has the most variability because the range, which is the difference between the highest and lowest score, is the highest among the given options. The range in option A is 19-7=12, whereas, in the other options, the range is much smaller. Option B has two repeated scores, which reduces the range. Option C has no variability, as all scores are the same. Option D has a smaller range than option A but still has some variability.

Question 8

The three measures of variability commonly used to reflect the spread or dispersion in a group of scores are the standard deviation, the variance, and the what?

Accepted Answer

The three measures of variability commonly used are the standard deviation, the variance, and the range. The range reflects the difference between the highest and lowest scores in a dataset, indicating the spread of the scores. Outliers are extreme values that lie far away from the majority of the data but are not a measure of variability. Skew measures the asymmetry of the data distribution and is not a measure of variability. Percentile is a measure of position and not a measure of variability.

Question 9

The average and which of the following can be used to describe the characteristics of a distribution and show how distributions differ from one another?

Accepted Answer

Variability, along with the average, helps describe the spread and differences in a distribution, unlike mode, median, or sum.

Question 10

If you intend to use a sample as an estimate of a population parameter, which standard deviation is the best to calculate?

Accepted Answer

The best standard deviation to use when estimating a population parameter from a sample is the unbiased standard deviation. This is because the unbiased standard deviation takes into account the fact that the sample is only a subset of the population and corrects for the tendency of the sample standard deviation to underestimate the population standard deviation. The other options (biased, squared deviation, and mean deviation) do not account for this and may lead to biased estimates.

Question 11

What is the formula for the exclusive range?

Accepted Answer

The exclusive range is calculated by subtracting the lowest value (l) from the highest value (h), which is represented by the formula h - l.

Question 12

What is the formula for the inclusive range?

Accepted Answer

The formula for the inclusive range is highest value (h) minus lowest value (l) plus one (h - l + 1). This is because there are h - l numbers within that range, but including the endpoints adds an extra number.

Question 13

What is the most frequently used measure of variability?

Accepted Answer

Standard deviation is the most commonly used measure of variability as it takes into account all the data points and provides a more accurate representation of the spread of data compared to range or mean deviation. Variance is also used, but standard deviation is preferred as it is easier to interpret since it is in the same unit as the data.

Question 14

In the formula for computing the range, what does the letter "h" represent?

Accepted Answer

The letter "h" in the formula for computing the range represents the highest score in the dataset. Therefore, the best choice is D.

Question 15

Variability is a measure of how much each score in a group of scores differs from the what?

Accepted Answer

Variability is measured by calculating the differences between each score and the mean. Therefore, the mean is the best measure of central tendency to use in calculating variability. The mode and median are not as useful since they only take into account the most common or middle values, respectively, and do not consider the entire range of scores. Choice C is erroneous and not an option.

Question 16

What is the term associated with scores that are at the extreme ends of the distribution?

Accepted Answer

Outliers are scores that are distant from the rest of the distribution and are often considered anomalous or unusual compared to the majority of the other scores. They can greatly impact the mean and standard deviation of a distribution and may require special attention during statistical analysis.

Question 17

If a distribution is "significantly distorted" what is this called?

Accepted Answer

When a distribution is "significantly distorted", it is referring to the presence of skewness. Skewness is a measure of the asymmetry of the distribution, where a positive skew indicates a longer tail on the right side of the distribution and a negative skew indicates a longer tail on the left side of the distribution. Therefore, the best choice is C, skew.

Question 18

What is obtained by squaring the standard deviation?

Accepted Answer

Squaring the standard deviation gives us the variance, which measures how far a set of numbers is spread out.

Question 19

Which of the following is one way to represent variance?

Accepted Answer

Variance is typically represented as the squared standard deviation, which is denoted by s². Choice A (s) is just the standard deviation, not the variance. Choice C is a random string of characters and not a standard notation for variance. Choice D is a formula for calculating the average, not the variance.

Question 20

When calculating the standard deviation, what must be done in order to obtain an unbiased estimate of the population?

Accepted Answer

In order to obtain an unbiased estimate of the population standard deviation, we must subtract 1 from the sample size (n), which is the correction factor for the fact that the sample standard deviation tends to underestimate the population standard deviation.

Quiz 3: Vive La Différence: Understanding Variability