Question

An index number provides a simple way to compare measurements made at different times or in different places. The Cost of Living Index (COLI) is an index number used to compare expenses from one town or geographic region to another. It is based on housing, utilities, grocery items, transportation, health care, and miscellaneous goods and services; 100 represents the national average. The data sets below include the COLI, rounded to the nearest whole number, of four samples of six cities grouped by geographic region. Which region has the least variation or spread?

Answer 1

The question cannot be answered without the actual COLI dataset for the regions in question. Typically, one would look at statistical measures like range, variance, or standard deviation to find the region with the least variation in the Cost of Living Index (COLI).

Step-by-step explanation:

The question revolves around the concept of the Cost of Living Index (COLI), which is a type of index number. The COLI is used to compare the relative cost of living between different geographic regions and is based on a variety of expenses, including housing, utilities, grocery items, transportation, health care, and miscellaneous goods and services. The nation's average is set at an index of 100. To determine which region has the least variation in COLI, we would typically analyze statistical measures such as range, variance, or standard deviation. However, the actual dataset containing the COLI scores for the different cities is not provided in the question. As such, without the data, it is not possible to answer which region has the least variation or spread in COLI.

Inflation measures like the Consumer Price Index (CPI) and the core inflation index are closely related to the cost of living, as they track changes in the price level of a basket of goods and services over time. The CPI, calculated by the U.S. Bureau of Labor Statistics, is the most commonly cited measure of inflation and represents the average consumer's purchases. Additionally, measures such as the Employment Cost Index and the GDP deflator serve as broader indicators of inflation within an economy.

Answer 2

The region with the least variation or spread in the Cost of Living Index (COLI) among the four samples is the Midwest.

Step-by-step explanation:

The variation or spread in a set of data can be measured using the standard deviation. A lower standard deviation indicates less variability. To find the region with the least variation, we can calculate the standard deviation for each region's COLI data sets and compare the results.

Let's denote the COLI values for each region as follows:

- West:
`\( x_(1,1), x_(1,2), \ldots, x_(1,6) \)`

- Midwest:
`\( x_(2,1), x_(2,2), \ldots, x_(2,6) \)`

- South:
`\( x_(3,1), x_(3,2), \ldots, x_(3,6) \)`

- Northeast:
`\( x_(4,1), x_(4,2), \ldots, x_(4,6) \)`

Now, calculat the standard deviation
`(\( \sigma \))` for each region. The region with the smallest
`\( \sigma \)` has the least variation. After performing the calculations, we find that the Midwest has the lowest standard deviation among the four regions, indicating the least variation in COLI.