Question 1

Which of the following is the lowest valid score for a standard deviation?

Accepted Answer

Standard deviation cannot be negative; the lowest valid score is 0, indicating no variability in the data set.

Question 2

Which of these statements describes the difference between variance and standard deviation?

Accepted Answer

Variance is the square of the standard deviation, so when variance is greater than 1, the standard deviation is smaller than the variance.

Question 3

Suppose low variability in a runner's heart rate during a long distance run is a good indication of cardiopulmonary fitness. Which of these statistics measuring pulse rates during a 20 km run would be best?

Accepted Answer

A lower standard deviation indicates less variability in the heart rate, suggesting better cardiopulmonary fitness.

Question 4

Suppose a distribution has an outlying value far smaller than the other values in the distribution. What will happen to the standard deviation if the outlier is removed?

Accepted Answer

Removing an outlier that is far from the other values typically reduces the spread of the data, leading to a decrease in the standard deviation.

Question 5

Researchers wish to compare the dispersion of student grades across eight universities of varying sizes. What strategy would allow them to properly compare grade dispersion across the eight distributions?

Accepted Answer

Dividing the squared deviations by the number of cases (N) for each university would allow the researchers to properly compare grade dispersion across the eight distributions, as this would standardize the variance for each distribution.

Question 6

What is the one central tendency statistic that can be accurately calculated for nominal, ordinal, and interval-ratio variables?

Accepted Answer

The mode is the only measure of central tendency that can be used with nominal, ordinal, and interval-ratio variables, as it simply identifies the most frequently occurring category or value.

Question 7

Table 3.1 Data Set of Six Volunteers at a Charitable Organization
 
-Refer to Table 3.1. What is the mode of employment status?

Accepted Answer

The mode is the category that appears most frequently. If "full-time worker" appears more frequently than other categories in Table 3.1, it is the mode.

Question 8

Table 3.1 Data Set of Six Volunteers at a Charitable Organization
 
-Refer to Table 3.1. What is the median of employment status?

Accepted Answer

The median is a measure of central tendency that requires numerical data. Employment status is categorical, so a median cannot be calculated.

Question 9

Table 3.1 Data Set of Six Volunteers at a Charitable Organization
 
-Refer to Table 3.1. What is the mean of years served in the organization?

Accepted Answer

The mean is calculated by summing all the years served and dividing by the number of data points. If the sum of years served is 15 and there are 5 data points, the mean is 15/5 = 3.

Question 10

Table 3.1 Data Set of Six Volunteers at a Charitable Organization
 
-Refer to Table 3.1. What is the median of years served in the organization?

Accepted Answer

The median is the middle value in a list of numbers. Without the actual data from Table 3.1, we assume the list is sorted. If the number of data points is even, the median is the average of the two middle numbers. If it's odd, it's the middle number. Here, 2.5 is likely the average of two middle values.

Question 11

Table 3.2 Park Space in Five Neighbourhoods of a Fictional City
 
-Refer to Table 3.2. Which of the following describes the distribution of park space?

Accepted Answer

The distribution of park space is negatively skewed because the mean (1.3 acres) is greater than the median (0.8 acres).

Question 12

Table 3.2 Park Space in Five Neighbourhoods of a Fictional City
 
-Refer to Table 3.2. What would be the most appropriate measure of central tendency for the distribution of park space?

Accepted Answer

The median is the most appropriate measure of central tendency for skewed distributions or when there are outliers, which is often the case with park space distributions.

Question 13

Table 3.3 Means and Standard Deviations in Monthly Accident Events for Two Mining Companies, 2014-2018
 
-Refer to Table 3.3. Which of the following could we conclude from these data?

Accepted Answer

The statement suggests that H & W Energy Resources had fewer accidents on average compared to Jackson Minerals, but experienced more variation in the number of accidents from month to month.

Question 14

Table 3.3 Means and Standard Deviations in Monthly Accident Events for Two Mining Companies, 2014-2018
 
-Refer to Table 3.3. What is the value for the variance of H & W Energy Resources?

Accepted Answer

The answer of Table 3.3 Means and Standard Deviations in...

Question 15

Describe what a boxplot portrays and explain what its "whiskers" are.

Accepted Answer

The answer of Describe what a boxplot portrays and explain...

Question 16

What is the difference between central tendency and dispersion in a distribution of data?

Accepted Answer

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

Question 17

The mayor of a city (City A) was wondering whether her city has shown that more new companies start up in City A than in another city of similar size. She asked her staff to gather the number of new companies started annually in her city from 2006 to 2017. She obtained similar data from her comparison city (City B). Compute the mode, mean, median, range, and standard deviation for both cities.

Accepted Answer

The answer of The mayor of a city (City A)...

Question 18

Below is a summary of data about violent crime rates (number of violent crimes per 100,000 population) for a sample of 20 cities in two different years. Describe this statistical information in words. What changes occurred in the overall shape of the distribution for this variable? In central tendency? In dispersion?

Accepted Answer

The answer of Below is a summary of data about...

Quiz 3: Measures of Central Tendency and Dispersion

Which of the following is the lowest valid score for a standard deviation?

Which of these statements describes the difference between variance and standard deviation?

Suppose low variability in a runner's heart rate during a long distance run is a good indication of cardiopulmonary fitness. Which of these statistics measuring pulse rates during a 20 km run would be best?

Suppose a distribution has an outlying value far smaller than the other values in the distribution. What will happen to the standard deviation if the outlier is removed?

Researchers wish to compare the dispersion of student grades across eight universities of varying sizes. What strategy would allow them to properly compare grade dispersion across the eight distributions?

What is the one central tendency statistic that can be accurately calculated for nominal, ordinal, and interval-ratio variables?

Table 3.1 Data Set of Six Volunteers at a Charitable Organization -Refer to Table 3.1. What is the mode of employment status?

Table 3.1 Data Set of Six Volunteers at a Charitable Organization -Refer to Table 3.1. What is the median of employment status?

Table 3.1 Data Set of Six Volunteers at a Charitable Organization -Refer to Table 3.1. What is the mean of years served in the organization?

Table 3.1 Data Set of Six Volunteers at a Charitable Organization -Refer to Table 3.1. What is the median of years served in the organization?

Table 3.2 Park Space in Five Neighbourhoods of a Fictional City -Refer to Table 3.2. Which of the following describes the distribution of park space?

Table 3.2 Park Space in Five Neighbourhoods of a Fictional City -Refer to Table 3.2. What would be the most appropriate measure of central tendency for the distribution of park space?

Table 3.3 Means and Standard Deviations in Monthly Accident Events for Two Mining Companies, 2014-2018 -Refer to Table 3.3. Which of the following could we conclude from these data?

Table 3.3 Means and Standard Deviations in Monthly Accident Events for Two Mining Companies, 2014-2018 -Refer to Table 3.3. What is the value for the variance of H & W Energy Resources?

Describe what a boxplot portrays and explain what its "whiskers" are.

What is the difference between central tendency and dispersion in a distribution of data?