To complete the grouped frequency distribution for the biology test scores, start by defining the group intervals (or ranges) for the test scores. Given a class width of 4, we can divide the scores into the following intervals:
1. 72 to 75
2. 76 to 79
3. 80 to 83
4. 84 to 87
5. 88 to 91
Next, we will count the number of scores that fall within each interval.
Here are the test scores provided:
73, 74, 86, 85, 78, 84, 80, 89, 77, 90, 79, 81, 78, 83, 74, 82
We can now assign the scores to the appropriate intervals and count them:
- For the interval 72 to 75:
- Scores: 73, 74, 74
- Frequency: 3 (indicated as [tex]\( U \)[/tex])
- For the interval 76 to 79:
- Scores: 78, 77, 79, 78
- Frequency: 4 (indicated as [tex]\( \Pi \)[/tex])
- For the interval 80 to 83:
- Scores: 80, 81, 83, 82
- Frequency: 4 (indicated as [tex]\(51\)[/tex])
- For the interval 84 to 87:
- Scores: 86, 85, 84
- Frequency: 3 (indicated as [tex]\(26\)[/tex])
- For the interval 88 to 91:
- Scores: 89, 90
- Frequency: 2 (indicated as [tex]\(12\)[/tex])
Finally, the completed grouped frequency distribution table is:
\begin{tabular}{|c|c|}
\hline Test scores & Frequency \\
\hline 72 to 75 & 3 \\
\hline 76 to 79 & 4 \\
\hline 80 to 83 & 4 \\
\hline 84 to 87 & 3 \\
\hline 88 to 91 & 2 \\
\hline
\end{tabular}
