Question 1

Which of the following variables has the greatest dispersion?

Accepted Answer

The standard deviation and variance both measure dispersion, but the standard deviation is a more intuitive and commonly used measure. The variable with the greatest standard deviation is variable D with a value of 6.

Question 2

Which of the following is a measure of central tendency?

Accepted Answer

Mode is a measure of central tendency which represents the most frequently occurring value in a dataset. Range, standard deviation, and variance are measures of variability or dispersion, not central tendency.

Question 3

If an ordinal variable has nine attributes, is the fifth attribute always the median? Explain your answer.

Accepted Answer

The answer of If an ordinal variable has nine attributes,...

Question 4

Scores on an exam had a mean of 75 and a standard deviation of 5. Which of the following statements is most likely to be true about the distribution of scores on the exam?

Accepted Answer

The standard deviation of 5 indicates that there is variability in the scores. Some students may have scored above the mean by more than 5 points, while others may have scored below the mean by more than 5 points. Therefore, option D is the most likely choice.

Question 5

You want a measure of dispersion for an interval/ratio level variable. You want the measure that makes use of the fact that the attributes are not only different and have rank order but also represent a numeric scale. What statistic would you calculate?

Accepted Answer

Standard deviation is the measure of dispersion which takes into account the fact that the variable is from an interval/ratio scale and has a numeric value assigned to each attribute. It measures the variability of data from the mean and indicates how spread out the data is.

Question 6

You have an interval/ratio variable. It is very negatively skewed. You want to report just one measure of central tendency. Which of the following is correct?

Accepted Answer

For a very negatively skewed distribution, the mean is pulled towards the tail with low values. The median is less affected by extreme values, making it a more representative measure of central tendency in this scenario.

Question 7

Name five different univariate descriptive statistics.

Accepted Answer

The answer of Name five different univariate descriptive statistics....

Question 8

If the mean on an exam was 75 and the standard deviation was 5, what do you know about the distribution of exam grades around the mean?

Accepted Answer

The answer of If the mean on an exam was...

Question 9

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

Accepted Answer

The lowest level of measurement that permits calculation of a mean is interval/ratio. This is because interval/ratio data involves numerical values that have a natural order, and the difference between values is meaningful. Nominal and ordinal data involve categories and rankings, respectively, which do not have numerical values that can be used to calculate a mean.

Question 10

Exactly half the class got a 70 on an exam and exactly half got a 90 on the exam. The median is

Accepted Answer

The median is the middle value when data is ordered. With half scoring 70 and half scoring 90, the median is the average of these two numbers: (70+90)/2 = 80.

Question 11

The admissions office has ordinal-level data on parental income levels of enrolled students. What would an appropriate measure of central tendency be to report?

Accepted Answer

Median would be the most appropriate measure of central tendency for ordinal-level data on parental income levels, as it would represent the exact middle value in the ranked list of incomes. The mean would not be appropriate as it assumes interval-level data and can be influenced by extreme outliers. Percent distribution would not provide a measure of central tendency, and standard deviation would not be appropriate without first converting the data to interval-level.

Question 12

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

Accepted Answer

A minimum can only be calculated if values can be arranged in a meaningful order, such as from smallest to largest. This is only possible with ordinal level of measurement. In nominal measurement, values do not have any order or relationship to each other, while in interval/ratio measurement, although there is a meaningful order, the zero point is arbitrary and should not be manipulated mathematically to calculate minimums.

Question 13

What is the difference between central tendency and dispersion?

Accepted Answer

The answer of What is the difference between central tendency...

Question 14

What measures of central tendency and dispersion only become available at the interval/ratio level of measurement?

Accepted Answer

The answer of What measures of central tendency and dispersion...

Question 15

A mean is

Accepted Answer

A mean is a type of central tendency measure that describes the average value of a set of numbers. It only describes one variable, making it a univariate descriptive statistic.

Question 16

The registrar has nominal-level data on students' racial classification. What would be an appropriate measure of central tendency to report?

Accepted Answer

Since racial classification is nominal-level data, it cannot be meaningfully averaged, so the mean is not appropriate. The median is also not applicable, as there is no inherent order to the categories of race. Instead, the mode, or the most frequent response, is the best measure of central tendency for nominal data. Alternatively, the percent distribution could be reported, but this would not be a measure of central tendency.

Question 17

What are three measures of central tendency? What are three measures of dispersion? Make it clear which are which.

Accepted Answer

The answer of What are three measures of central tendency?...

Question 18

You want a measure of central tendency for an ordinal level variable. You want the measure that makes use of the fact that the attributes are not only different but also have rank order. What statistic would you calculate?

Accepted Answer

The median is the best choice for measuring central tendency for an ordinal level variable as it takes into account the rank order of the attributes. The mean is not appropriate for ordinal data because there is no meaningful way to add or subtract the attributes. The range and standard deviation are measures of variability and do not take into account the rank order of the attributes.

Question 19

You want to see the mean, standard deviation, minimum, and maximum for a variable. Which SPSS procedure would be most appropriate?

Accepted Answer

The Frequencies procedure allows you to generate descriptive statistics such as mean, standard deviation, minimum, and maximum for a variable.

Question 20

You want to see the mode and percent distribution for a variable. Which SPSS procedure would be most appropriate?

Accepted Answer

The Frequencies procedure in SPSS provides the mode, as well as the percent distribution of a variable. Therefore, it is the most appropriate procedure for this task.

Quiz 4: Central Tendency and Dispersion