Questions: Question The Bureau of Labor Statistics compiles and makes publicly available data from a range of different sectors of the economy. One value that is reported is a weighted average of the costs of certain goods, called the Consumer Price Index (CPI). The CPI is related to the price but is not a dollar amount. The rise in prices is used as a metric of inflation. To make the metric more reliable, a chained CPI was created. The regular CPI does not update the types of goods it averages often enough to reflect the market trends, like a switch from apples to oranges resulting from a rise in apple prices. The chained CPI is a measure of price that takes this into account, and there are several bills that are tied to the chained CPI index in order to determine the payout the bill allots each year. The monthly average chained CPI for urban apparel for all urban consumers for 10 consecutive months is provided below. The data are not seasonally adjusted. Construct a box and whisker plot using a TI-83, TI-83 Plus, or T1-84 graphing calculator to choose the correct plot below. All plots have the following window settings: X min =88, X max =100.5, Xscl=0.5, Y min =-0.5, Y max =3.5, Yscl=1, Xres=1 Chained CPI - Apparel - 89.02 - 89.10 - 90.06 - 90.54 - 91.31 - 91.69 - 91.85 - 94.76 - 95.18 - 99.51

Question
The Bureau of Labor Statistics compiles and makes publicly available data from a range of different sectors of the economy. One value that is reported is a weighted average of the costs of certain goods, called the Consumer Price Index (CPI). The CPI is related to the price but is not a dollar amount. The rise in prices is used as a metric of inflation. To make the metric more reliable, a chained CPI was created. The regular CPI does not update the types of goods it averages often enough to reflect the market trends, like a switch from apples to oranges resulting from a rise in apple prices. The chained CPI is a measure of price that takes this into account, and there are several bills that are tied to the chained CPI index in order to determine the payout the bill allots each year. The monthly average chained CPI for urban apparel for all urban consumers for 10 consecutive months is provided below. The data are not seasonally adjusted. Construct a box and whisker plot using a TI-83, TI-83 Plus, or T1-84 graphing calculator to choose the correct plot below. All plots have the following window settings: X min =88, X max =100.5, Xscl=0.5, Y min =-0.5, Y max =3.5, Yscl=1, Xres=1

Chained CPI - Apparel
- 89.02
- 89.10
- 90.06
- 90.54
- 91.31
- 91.69
- 91.85
- 94.76
- 95.18
- 99.51
Transcript text: Question The Bureau of Labor Statistics compiles and makes publicly available data from a range of different sectors of the economy. One value that is reported is a weighted average of the costs of certain goods, called the Consumer Price Index (CPI). The CPI is related to the price but is not a dollar amount. The rise in prices is used as a metric of inflation. To make the metric more reliable, a chained CPI was created. The regular CPI does not update the types of goods it averages often enough to reflect the market trends, like a switch from apples to oranges resulting from a rise in apple prices. The chained CPI is a measure of price that takes this into account, and there are several bills that are tied to the chained CPI index in order to determine the payout the bill allots each year. The monthly average chained CPI for urban apparel for all urban consumers for 10 consecutive months is provided below. The data are not seasonally adjusted. Construct a box and whisker plot using a TI-83, TI-83 Plus, or T1-84 graphing calculator to choose the correct plot below. All plots have the following window settings: $\mathrm{X} \min =88, \mathrm{X} \max =100.5, \mathrm{Xscl}=0.5, \mathrm{Y} \min =-0.5, \mathrm{Y} \max =3.5, \mathrm{Yscl}=1, \mathrm{Xres}=1$ \begin{tabular}{|c|} \hline Chained CPI - Apparel \\ \hline 89.02 \\ \hline 89.10 \\ \hline 90.06 \\ \hline 90.54 \\ \hline 91.31 \\ \hline 91.69 \\ \hline 91.85 \\ \hline 94.76 \\ \hline 95.18 \\ \hline 99.51 \\ \hline \end{tabular}
failed

Solution

failed
failed

Solution Steps

To construct a box and whisker plot, we need to determine the five-number summary of the data: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. These values will help us visualize the distribution of the data.

Step 1: Organize the Data

First, list the given data in ascending order:

\[ 89.02, 89.10, 90.06, 90.54, 91.31, 91.69, 91.85, 94.76, 95.18, 99.51 \]

Step 2: Calculate the Five-Number Summary
  1. Minimum: The smallest value is \(89.02\).
  2. Maximum: The largest value is \(99.51\).
  3. Median: The median is the middle value. Since there are 10 data points, the median is the average of the 5th and 6th values: \[ \text{Median} = \frac{91.31 + 91.69}{2} = 91.50 \]
  4. First Quartile (Q1): The median of the first half of the data (first 5 values): \[ Q1 = \text{Median of } (89.02, 89.10, 90.06, 90.54, 91.31) = 90.06 \]
  5. Third Quartile (Q3): The median of the second half of the data (last 5 values): \[ Q3 = \text{Median of } (91.69, 91.85, 94.76, 95.18, 99.51) = 94.76 \]
Step 3: Construct the Box and Whisker Plot

Using the five-number summary:

  • Minimum: \(89.02\)
  • Q1: \(90.06\)
  • Median: \(91.50\)
  • Q3: \(94.76\)
  • Maximum: \(99.51\)

Final Answer

The box and whisker plot is constructed using the five-number summary:

  • Minimum: \(89.02\)
  • Q1: \(90.06\)
  • Median: \(91.50\)
  • Q3: \(94.76\)
  • Maximum: \(99.51\)

\[ \boxed{\text{Minimum: } 89.02, \, Q1: 90.06, \, \text{Median: } 91.50, \, Q3: 94.76, \, \text{Maximum: } 99.51} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful