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Find the mode for the data items in the given frequency distribution.

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
Score, [tex]$x$[/tex] & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline
Frequency, [tex]$f$[/tex] & 1 & 1 & 1 & 3 & 8 & 7 & 4 & 4 & 4 & 1 \\
\hline
\end{tabular}

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The mode(s) is/are [tex]$\square$[/tex] (Use a comma to separate answers as needed.)

B. There is no mode.



Answer :

GinnyAnswer
To find the mode of the given frequency distribution, follow these steps:

1. Identify the frequencies of each score:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \text{Score}, \, x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline \text{Frequency}, \, f & 1 & 1 & 1 & 3 & 8 & 7 & 4 & 4 & 4 & 1 \\ \hline \end{array} \][/tex]

2. Recognize the highest frequency in the distribution. Here, the highest frequency is 8.

3. Identify the score(s) corresponding to this highest frequency. By examining the table, the score corresponding to the highest frequency of 8 is [tex]\(5\)[/tex].

Thus, the mode for this frequency distribution is the score [tex]\(5\)[/tex], because it appears more frequently than any other score.

Therefore, the answer is:

A. The mode(s) is/are [tex]\(5\)[/tex].

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