Questions: for Liberal Arts (3 cr) - Garey Matsuyama Homework Question 16, 12.2.ICV1 Part 3 of 7 Watch the video and then complete parts (a) through (g) below. Click here to watch the video. Use the frequency distribution to the right to complete parts (a) through ( g ). x f 10 2 14 5 15 6 20 5 25 2 (a) List the items in the data set in numerical order. List each item as many times as it appears in the set. A. 2,2,5,5,6 B. 10,10,14,14,14,14,14,15,15,15,15,15,15,20,20,20,20,20,25,25 C. 10,14,15,20,25 D. 2,2,2,2,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6 (b) What is the mode of the data set? 15 (Type a whole number.) (c) How can the mode of any frequency distribution be identified? A. The highest value in the data column B. The value in the data column corresponding to the highest value in the frequency column C. The sum of the values in the frequency column D. The highest value in the frequency column

for Liberal Arts (3 cr) - Garey Matsuyama Homework Question 16, 12.2.ICV1 Part 3 of 7 Watch the video and then complete parts (a) through (g) below. Click here to watch the video. Use the frequency distribution to the right to complete parts (a) through ( g ). x f 10 2 14 5 15 6 20 5 25 2 (a) List the items in the data set in numerical order. List each item as many times as it appears in the set. A. 2,2,5,5,6 B. 10,10,14,14,14,14,14,15,15,15,15,15,15,20,20,20,20,20,25,25 C. 10,14,15,20,25 D. 2,2,2,2,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6 (b) What is the mode of the data set? 15 (Type a whole number.) (c) How can the mode of any frequency distribution be identified? A. The highest value in the data column B. The value in the data column corresponding to the highest value in the frequency column C. The sum of the values in the frequency column D. The highest value in the frequency column
Transcript text: for Liberal Arts (3 cr) - Garey Matsuyama Homework Question 16, 12.2.ICV1 Part 3 of 7 Watch the video and then complete parts (a) through (g) below. Click here to watch the video. Use the frequency distribution to the right to complete parts (a) through ( g ). \begin{tabular}{|c|c|} \hline $\mathbf{x}$ & $\mathbf{f}$ \\ \hline 10 & 2 \\ \hline 14 & 5 \\ \hline 15 & 6 \\ \hline 20 & 5 \\ \hline 25 & 2 \\ \hline \end{tabular} (a) List the items in the data set in numerical order. List each item as many times as it appears in the set. A. $\{2,2,5,5,6\}$ B. $\{10,10,14,14,14,14,14,15,15,15,15,15,15,20,20,20,20,20,25,25\}$ C. $\{10,14,15,20,25\}$ D. $\{2,2,2,2,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6\}$ (b) What is the mode of the data set? 15 (Type a whole number.) (c) How can the mode of any frequency distribution be identified? A. The highest value in the data column B. The value in the data column corresponding to the highest value in the frequency column C. The sum of the values in the frequency column D. The highest value in the frequency column
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Solution

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Solution Steps

Solution Approach

(a) To list the items in the data set in numerical order, we need to expand the frequency distribution table into a full list of data points. Each value \( x \) should be repeated according to its frequency \( f \).

(b) The mode of the data set is the value that appears most frequently. We can determine this by identifying the value with the highest frequency in the frequency distribution.

(c) The mode of any frequency distribution can be identified by finding the value in the data column that corresponds to the highest frequency in the frequency column.

Step 1: Constructing the Data Set

From the given frequency distribution:

\[ \begin{array}{|c|c|} \hline x & f \\ \hline 10 & 2 \\ 14 & 5 \\ 15 & 6 \\ 20 & 5 \\ 25 & 2 \\ \hline \end{array} \]

We expand this into a complete data set by repeating each value \( x \) according to its frequency \( f \):

\[ \text{Data set} = \{10, 10, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 20, 20, 20, 20, 20, 25, 25\} \]

Step 2: Sorting the Data Set

The data set in numerical order is:

\[ \text{Sorted Data Set} = \{10, 10, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 20, 20, 20, 20, 20, 25, 25\} \]

Step 3: Finding the Mode

The mode is the value that appears most frequently in the data set. From the frequency distribution, we see that:

\[ \text{Mode} = 15 \quad (\text{appears } 6 \text{ times}) \]

Step 4: Identifying the Mode in Frequency Distribution

The mode can be identified as the value in the data column corresponding to the highest value in the frequency column. Thus, the method to identify the mode is:

\[ \text{Mode Identification Method} = \text{The value in the data column corresponding to the highest value in the frequency column} \]

Final Answer

  • The data set in numerical order is: \(\{10, 10, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 20, 20, 20, 20, 20, 25, 25\}\)
  • The mode of the data set is: \(\boxed{15}\)
  • The mode identification method is: \(\text{The value in the data column corresponding to the highest value in the frequency column}\)
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