Exam 3: Measures of Central Tendency and Dispersion

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?

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?

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

Environmental violations for 16 companies ranged from values of 11 to 97. The variance was 14. How should we calculate the standard deviation for this distribution?

Suppose you rank-ordered a set of 49 scores. What would be the median?

A small-scale coffee producer sent out the following number of bags of coffee beans each week over the course of last June: 6, 8, 10, 17. What is the median weekly value for that month?

A researcher reports that $18,000 represents the first quartile of Canadians' incomes. Which of the following is another term he could use to describe that dollar value?

Suppose we have yearly unemployment data for OECD countries. Which measure of central tendency would be the most appropriate for this data set?

A researcher asked 12 people in an apartment building what was their social class: upper-, middle-, or lower-class. What would be an appropriate measure of central tendency for this distribution?

What would be an appropriate measure of dispersion for a set of values of people's ages, measured in years?

Which index of qualitative variation scores shows the least amount of variation in a distribution?

Which of the following is among the problems with using the range (R) as a measure of dispersion?

How does the standard deviation formula differ for samples and populations?

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?

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.

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?

When would it be especially appropriate to rely on the interquartile range rather than the range to describe a sample's distribution?

What is the term for a distribution that has its peak on the left and a tail extending far to the right?

The distribution of film genre preferences in a retirement community of 150 seniors is as follows: Drama-37%; Comedy-32%; Musicals-8%; Action-18%; Documentaries-5%. Why is it impossible to calculate a standard deviation for this variable?

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