1.7.2: Exercise N.7

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The following table shows the average price per gallon of regular gasoline in U.S. cities,²⁴ and the price index for petroleum imports to the United States.²⁵ The Petroleum Import Price Index measures the change in international value of the crude petroleum that is imported to the United States. Petroleum can be refined and distilled to create a variety of fuels, including gasoline, or other industrial chemicals.

	Average Gas Price (Annual)	Petroleum Import Price Index (June)
2012	$3.680	357.2
2013	$3.575	364.9
2014	$3.437	387.9
2015	$2.520	226.1
2016	$2.250	173.1
2017	$2.528	178.7
2018	$2.813	255.4
2019	$2.691	236.6
2020	$2.258	142.6
2021	$3.100	267.6
2022	$4.059	456.5

(1) (a) Using the data from the two consecutive years 2019-2020, calculate the relative changes in gas price and petroleum import price. Round to the nearest hundredth of a percent.

(b) Using the data from the two consecutive years 2020-2021, calculate the relative changes in gas
price and petroleum import price. Round to the nearest hundredth of a percent.

The term volatility refers to the likelihood that something will change rapidly and unpredictably. Something with a price or value that varies greatly over time may be called volatile. Investors consider volatility when making investment decisions. An investor who takes risks, for example, might be interested in volatile stocks because the risk of a big decrease in value is outweighed by a chance for a big increase in value. A more conservative investor would avoid volatile stocks and look instead for something with a steadier value over time. Investors can also invest in commodities, such as crude oil, gold, and corn.

(2) Which of the two commodities in the table above, gas or import petroleum, could be described as more volatile? Please explain your reasoning using the Writing Principle

(3) With reference to the table above, calculate the overall relative changes from 2012 to 2022. Round your answers to the nearest hundredth of a percent.

(i) Overall relative change of the average gas price:

(ii) Overall relative change of the petroleum import price index:

In this collaboration, you used indices to compare how different salaries changed over time. Other kinds of indices can be used to make comparisons between other kinds of varying quantities. The Uniform Crime Reporting Program (https://ucr.fbi.gov) and the Bureau of Justice Statistics (www.bjs.gov) provide information and quantitative data about crime. Crime statistics are often reported as a “rate per 100,000 people” to help compare small percents. For example, in the table below, a robbery rate can be calculated by comparing the number of robberies in a year to the total population in that area, but these percentages can be very small and hard to compare. So the rate is then used to calculate how many people out of 100,000 would be a victim of robbery.

Estimated Crime in 2020²⁶

State	Population	Number of Robberies	Robbery Rate (as a percentage, rounded to the nearest ten thousandth)	Robbery Rate (per 100,000 people, rounded to the nearest tenth)
Montana	1,084,225	280	0.0258%	25.8
North Dakota	779,094	153	0.0197%	19.7
Vermont	643,077	66	0.0103%	10.3

Notice that we can use this table to conclude that these three states have nearly the same low robbery rate.

Now answer Questions 4-13 to complete the table below and write two or three sentences to summarize the data using the robbery rate per 100,000 people.

Estimated Crime in 2020²⁷

State	Population	Number of Robberies	Robbery Rate (as a percentage, rounded to the nearest ten thousandth of a percent)	Robbery Rate (per 100,000 people, rounded to the nearest tenth)
California	39,538,223	44,915	(4)	(5)
District of Columbia	689,545	2,295	(6)	(7)
Minnesota	5,706,494	3,909	(8)	(9)
New York	20,201,249	18,302	(10)	(11)
Ohio	11,799,448	7,894	(12)	(13)