Question 1

A variable that has a bimodal distribution

Accepted Answer

A bimodal distribution has two distinct modes, which means that there are two values that occur most frequently in the data. Therefore, option B is the correct answer. Option A is not correct because a bimodal distribution by definition has two modes. Options C and D are not correct because the skewness of a distribution does not necessarily have any relation to whether it is bimodal or not.

Question 2

What is the lowest level of measurement for which it is permissible to calculate a median?

Accepted Answer

The median is a measure of central tendency that is appropriate for ordinal data, as it can be calculated based on the relative position of values in the data set. In nominal data, there is no natural ordering of categories, and in interval/ratio data, the median may not accurately reflect the magnitude of differences between values. Therefore, the lowest level of measurement for which it is permissible to calculate a median is ordinal.

Question 3

You want to know the approximate average distance of cases from the mean on a particular variable. What statistic would you calculate?

Accepted Answer

Standard deviation is the measure of the average distance of all scores from the mean. It provides a more precise estimate of the dispersion of data around the mean than range or variance. The median is a measure of central tendency and does not represent the spread of the data. Therefore, option C is the best choice for this scenario.

Question 4

It is customary when describing the scores on an interval/ratio variable to report the values of which four statistics?

Accepted Answer

When describing the scores on an interval/ratio variable, it is customary to report the mean (average), standard deviation (spread of data), minimum (lowest score), and maximum (highest score). These four statistics provide a good summary of the distribution of the data. The other answer choices either include irrelevant statistics (e.g., mode, range) or do not include important statistics (e.g., minimum, maximum).

Question 5

Which of the following is a univariate statistic?

Accepted Answer

All of the options listed, mean, range, and variance, are univariate statistics because they each describe or summarize data from a single variable.

Question 6

It is customary when describing the scores on an ordinal variable to report the values of which three statistics?

Accepted Answer

Since the variable is ordinal, it does not have a meaningful mean or standard deviation. Therefore, reporting the median, minimum, and maximum values provides the most insightful description of the scores on the ordinal variable. The mode may also be useful, but it is not as informative as the minimum and maximum values.

Question 7

If the standard deviation in commuting time to work is 9 minutes, the variance is

Accepted Answer

The variance is equal to the standard deviation squared, so the variance in this case would be 9^2 which equals 81. Therefore, option D is the correct answer.

Question 8

Which of the following is correct?

Accepted Answer

The answer of Which of the following is correct?
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Question 9

Which of the following is a measure of dispersion?

Accepted Answer

The measure of dispersion refers to how spread out a set of data is. Percentiles are a measure of dispersion as they divide the data into portions and indicate how values are distributed throughout the range. The mean, median, and mode are measures of central tendency and do not provide information on dispersion.

Question 10

For interval/ratio data that is very positively skewed (that is, there are a few cases with extremely high values), the value of the mean will be _____ the value of the median.

Accepted Answer

For very positively skewed data, the mean is pulled in the direction of the skew more than the median, resulting in the mean being greater than the median.

Question 11

The scores on an interval/ratio variable are very positively skewed. Most of the cases on the variable have values _____ the mean. If you are reporting just one measure of central tendency, it should be the _____.

Accepted Answer

Since the variable is very positively skewed, most of the scores will be below the mean, and the median will be a better measure of central tendency than the mean. Therefore, choice D (below the median) is the best choice.

Question 12

When the scores on an interval/ratio variable are very negatively skewed, there are

Accepted Answer

When the scores on an interval/ratio variable are very negatively skewed, it indicates that there are a few extremely low scores. This type of skewness is caused by a few outliers that drag the distribution to the left.

Question 13

What is the lowest level of measurement for which it is permissible to calculate a mode?

Accepted Answer

The mode is the most frequently occurring value in a dataset. It can be calculated for any level of measurement, but the lowest level for which it is permissible to calculate a mode is nominal. In nominal data, the values are categorical and do not have a numeric ranking, so only the frequency of each category can be determined.

Question 14

If everyone in a class of 35 students got an exam score of 75, the value of the variance would be

Accepted Answer

If every student got the same score, there is no variation in the data. Variance measures how spread out a set of data is, so in this case, the variance would be 0.

Question 15

What is the lowest level of measurement for which it is permissible to calculate a variance?

Accepted Answer

Variance can only be calculated for interval/ratio level of measurement where the values have a meaningful numerical order and a constant unit of measurement. Nominal and ordinal levels of measurement do not have such properties.

Question 16

A standard deviation is

Accepted Answer

A standard deviation is a measure of dispersion or spread of a single variable, hence it is a univariate descriptive statistic. A multivariate statistic would involve analyzing relationships between multiple variables, while inferential statistics involve using sample data to make inferences about a population.

Question 17

At Company A employees commute an average of 25 miles and the standard deviation is 10 miles. At Company B employees commute an average of 50 miles and the standard deviation is 5 miles. At which company is there more dispersion in commuting distances?

Accepted Answer

Dispersion is measured by the standard deviation. Company A has a higher standard deviation (10 miles) compared to Company B (5 miles), indicating more dispersion in commuting distances at Company A.

Question 18

What do measures of central tendency communicate about the scores on a variable?

Accepted Answer

Measures of central tendency, such as mean, median, and mode, communicate the typical score on a variable. They do not convey information about the difference, diversity, or variability of scores, which are communicated by measures of dispersion.

Question 19

A researcher has a nominal level variable. Which of the following would be an acceptable way to discuss its dispersion?

Accepted Answer

For nominal level variables, which are categorical and do not have a natural order, discussing dispersion in terms of percentage distribution is appropriate. This method allows for the representation of how frequently each category occurs relative to the others. Standard deviation, minimum and maximum, and range are measures used for interval or ratio level data, which have a meaningful order and fixed intervals.

Question 20

To locate the range in which the middle 80% of the class scored on an exam, you would want to see which percentiles?

Accepted Answer

The middle 80% of scores would exclude the lowest 10% and the highest 10% of scores, thus ranging from the 10th to the 90th percentile.

Quiz 4: Central Tendency and Dispersion