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There were 20 participants in a recent study on personality traits. After being shown five images (1, 2, 3, 4, and 5), each participant selected the one that was most appealing to them.

(a) The image each participant selected appears below. Complete the frequency distribution for the data.

[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
2 & 5 & 3 & 1 & 2 \\
1 & 3 & 4 & 2 & 4 \\
5 & 5 & 2 & 5 & 2 \\
3 & 2 & 3 & 4 & 1 \\
\hline
\end{tabular}
\][/tex]

[tex]\[
\begin{tabular}{|c|c|}
\hline
Image & Frequency \\
\hline
1 & $\square$ \\
2 & $\square$ \\
3 & $\square$ \\
4 & $\square$ \\
5 & $\square$ \\
\hline
\end{tabular}
\][/tex]



Answer :

GinnyAnswer
Sure, let's complete the frequency distribution of the images selected by the participants.

First, we need to count the frequency of each image selection. The images selected by the participants are listed as follows:

[tex]\[ \begin{tabular}{|lllll|} \hline 2 & 5 & 3 & 1 & 2 \\ 1 & 3 & 4 & 2 & 4 \\ 5 & 5 & 2 & 5 & 2 \\ 3 & 2 & 3 & 4 & 1 \\ \hline \end{tabular} \][/tex]

To count the frequency, we tally how many times each image appears in this list.

1. Image 1:
- Appears 3 times (row 1, column 4; row 2, column 1; row 4, column 5)

2. Image 2:
- Appears 6 times (row 1, columns 1 and 5; row 2, column 3; row 3, columns 3 and 5; row 4, column 2)

3. Image 3:
- Appears 4 times (row 1, column 3; row 2, column 2; row 4, columns 1 and 3)

4. Image 4:
- Appears 3 times (row 2, columns 3 and 5; row 4, column 4)

5. Image 5:
- Appears 4 times (row 1, column 2; row 3, columns 1, 2, and 4)

We can now complete the frequency distribution table:

[tex]\[ \begin{tabular}{cc} \textbf{Image} & \textbf{Frequency} \\ \hline 1 & 3 \\ 2 & 6 \\ 3 & 4 \\ 4 & 3 \\ 5 & 4 \\ \end{tabular} \][/tex]

So, the frequency distribution for the images selected by participants is:

- Image 1: 3
- Image 2: 6
- Image 3: 4
- Image 4: 3
- Image 5: 4

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