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A frequency table lists the elements in the sample space (the categories) and the frequency in which they occur. We discussed frequency tables in Unit 2 when we studied censuses and samples (Lesson 2.1: Overview of Statistics). In that lesson, we made tables that displayed tally marks, frequencies, and relative frequencies.

We will now use the table in the Gizmo to fill in the "Number of Votes" column of the table below. As a reminder of how to use tally marks, change the Display in the Gizmo to "Tally" to see how each vote was counted using tally marks. Recall that tallies are grouped by 5's (4 vertical lines crossed by a diagonal line) to make them easier to count. We will not use tallies on our frequency table since the number of votes for each category is provided on the table in the Gizmo. Fill in the "Number of Votes" column now.

You will now fill in the last column (Portion of the Vote (Relative frequency)) of the chart below. This information is not provided in the Gizmo, so we will have to rely on our knowledge of relative frequency from Unit 2. For this relative frequency, we will divide the number of votes for each mascot by the total votes cast. The relative frequency of Eagle votes has been provided.

For the remaining entries, enter the reduced fraction (using / for the division bar), then the decimal, and finally the percentage (be sure to include \%). Do not use spaces in your answers.

\begin{tabular}{|c|c|c|c|c|c|}
\hline
Mascot & \begin{tabular}{l} Number of Votes \\ (Frequency) \end{tabular} & \multicolumn{4}{|c|}{\begin{tabular}{l} Portion of Votes \\ (Relative Frequency) \\ Fraction [tex]$=$[/tex] Decimal [tex]$=$[/tex] Percent \end{tabular}} \\
\hline
Eagle & 15 & \multicolumn{4}{|c|}{\begin{tabular}{l} [tex]$\frac{15}{100}=\frac{3}{20}=0.15=15 \%$[/tex] \end{tabular}} \\
\hline
Lion & 44 & [tex]$\frac{44}{100}$[/tex] & 0.44 & [tex]$=$[/tex] & [tex]$44 \%$[/tex] \\
\hline
Bear & 26 & [tex]$\frac{26}{100}$[/tex] & 0.26 & [tex]$=$[/tex] & [tex]$26 \%$[/tex] \\
\hline
Wolf & 15 & [tex]$\frac{15}{100}$[/tex] & 0.15 & [tex]$=$[/tex] & [tex]$15 \%$[/tex] \\
\hline
Total & 100 & [tex]$=$[/tex] & & [tex]$=$[/tex] & [tex]$100 \%$[/tex] \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Certainly! Let's carefully fill in the table step-by-step using the given information.

We already know the number of votes for each mascot and the total number of votes. To find the relative frequency, we will calculate the fraction by dividing each number of votes by the total votes. This fraction will then be converted into a decimal and a percentage.

1. Eagle Votes:
- Number of Votes: 15
- Relative Frequency:
[tex]\[ \frac{15}{100} = 0.15 = 15\% \][/tex]

2. Lion Votes:
- Number of Votes: 44
- Relative Frequency:
[tex]\[ \frac{44}{100} = 0.44 = 44\% \][/tex]

3. Bear Votes:
- Number of Votes: 26
- Relative Frequency:
[tex]\[ \frac{26}{100} = 0.26 = 26\% \][/tex]

4. Wolf Votes:
- Number of Votes: 15
- Relative Frequency:
[tex]\[ \frac{15}{100} = 0.15 = 15\% \][/tex]

5. Total Votes:
- Number of Votes: 100
- Relative Frequency:
[tex]\[ \frac{100}{100} = 1.0 = 100\% \][/tex]

Let's place these calculations into the table format required:

[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Mascot} & \begin{array}{l} \text{Number of Votes} \\ \text{(Frequency)} \end{array} & \multicolumn{4}{|c|}{\begin{array}{c} \text{Portion of Votes} \\ \text{(Relative Frequency)} \\ \text{Fraction} = \text{Decimal} = \text{Percent} \end{array}} \\ \hline \text{Eagle} & 15 & \multicolumn{4}{|c|}{ \frac{15}{100} = \frac{3}{20} = 0.15 = 15\% } \\ \hline \text{Lion} & 44 & \multicolumn{4}{|c|}{ \frac{44}{100} = 0.44 = 44\% } \\ \hline \text{Bear} & 26 & \multicolumn{4}{|c|}{ \frac{26}{100} = 0.26 = 26\% } \\ \hline \text{Wolf} & 15 & \multicolumn{4}{|c|}{ \frac{15}{100} = 0.15 = 15\% } \\ \hline \text{Total} & 100 & \multicolumn{4}{|c|}{ \frac{100}{100} = 1.0 = 100\% } \\ \hline \end{array} \][/tex]

In summary, the completed table with the number of votes and their relative frequencies is shown above. Each mascot's relative frequency has been carefully calculated and presented as a fraction, a decimal, and a percent.