Answered

The stemplot displays the selling prices of homes for ABC Realty in April.




\multicolumn{5}{|l|}{Home Sale Data for ABC Realty}

0		678592

1		23818196

2		1325767787

3

4		5982

\multicolumn{3}{|c|}{Key: $1 \mid 23=$}		\multicolumn{3}{|l|}{\$123,000}






Select the correct set of data for the stemplot.


A\$459,000, \$277,000, \$67,000, \$123,000, \$213,000, \$482,000, \$85,000, \$181,000, \$300,000, \$225,000, \$92,000, \$181,000, \$287,000, \$196,000, \$276,000
B\$459,000, \$277,000, \$67,000, \$123,000, \$213,000, \$482,000, \$85,000, \$225,000, \$92,000, \$181,000, \$287,000, \$196,000, \$276,000
C\$459,000, \$277,000, \$67,000, \$123,000, \$213,000, \$482,000, \$85,000, \$181,000, \$225,000, \$92,000, \$181,000, \$287,000, \$196,000, \$276,000

Verified Answer :

  • Analyze the stemplot key: \(1 \mid 23 = \$123,000\) establishes the scale.
  • Extract all 14 data points: \(\$67,000, \$85,000, \$92,000, \$123,000, \$181,000, \$181,000, \$196,000, \$213,000, \$225,000, \$276,000, \$277,000, \$287,000, \$459,000, \$482,000\).
  • Compare the list against the provided options.
  • Choose the third option as it matches all extracted data points exactly.
  • Final Answer: Option 3.

Explanation

  1. Understanding the stemplot key

To interpret the stemplot, we first understand the key: \(1 \mid 23 = \$123,000\). This tells us that the stem value (left column) represents the hundred-thousands place, and the leaf values (the digits to the right) represent the combined remainder of the thousands, forming a total value in thousands of dollars. Specifically, for any row with stem \(s\) and leaves \(L\), the home sale price is \(\$(s \times 100 + L) \times 1,000\).

  1. Extracting the data set from the stemplot

We now extract each data point from the stemplot row by row:

  • Stem 0: \(0|67\), \(0|85\), \(0|92\) correspond to \(\$67,000\), \(\$85,000\), and \(\$92,000\).
  • Stem 1: \(1|23\), \(1|81\), \(1|81\), \(1|96\) correspond to \(\$123,000\), \(\$181,000\), \(\$181,000\), and \(\$196,000\).
  • Stem 2: \(2|13\), \(2|25\), \(2|76\), \(2|77\), \(2|87\) correspond to \(\$213,000\), \(\$225,000\), \(\$276,000\), \(\$277,000\), and \(\$287,000\).
  • Stem 3: Empty, so no values.
  • Stem 4: \(4|59\), \(4|82\) correspond to \(\$459,000\) and \(\$482,000\).

This results in a total of \(14\) data points.

  1. Identifying the correct option

We compare our list of 14 values against the provided options:

  1. Option 1 contains 15 values, including an extraneous \(\$300,000\), which does not appear in the stemplot.
  2. Option 2 contains only 13 values, missing one of the two \(\$181,000\) entries.
  3. Option 3 contains exactly the 14 values we derived: \(\$459,000, \$277,000, \$67,000, \$123,000, \$213,000, \$482,000, \$85,000, \$181,000, \$225,000, \$92,000, \$181,000, \$287,000, \$196,000, \$276,000\).

Therefore, Option 3 is the correct representation of the data.

Examples

Stem-and-leaf plots are a great way to organize numerical data so that you can quickly see the distribution of values. For example, if you were managing sales prices for a store or tracking scores on a test, a stemplot allows you to quickly identify the range (minimum to maximum) and spot any patterns or clusters in the data without needing to sort a long list of numbers manually. By understanding how to read these plots, you gain a powerful tool for initial data analysis in any real-world setting where numerical data is collected.

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