Sure, let's construct a grouped frequency distribution for the given IQ scores with class intervals starting at [tex]\(85-89\)[/tex] and subsequent intervals having the same width.
First, identify the class intervals:
1. [tex]\(85-89\)[/tex]
2. [tex]\(90-94\)[/tex]
3. [tex]\(95-99\)[/tex]
4. [tex]\(100-104\)[/tex]
5. [tex]\(105-109\)[/tex]
6. [tex]\(110-114\)[/tex]
7. [tex]\(115-119\)[/tex]
Next, determine the frequency (number of occurrences) of IQ scores within each class interval.
- For the interval [tex]\(85-89\)[/tex]: [tex]\( \{86, 86, 89, 87, 87, 89, 87, 89, 87 \} \rightarrow 9\)[/tex]
- For the interval [tex]\(90-94\)[/tex]: [tex]\( \{92, 92, 91, 90 \} \rightarrow 4\)[/tex]
- For the interval [tex]\(95-99\)[/tex]: [tex]\( \{96, 98, 96, 96, 97 \} \rightarrow 5\)[/tex]
- For the interval [tex]\(100-104\)[/tex]: [tex]\( \{100, 100, 101, 103, 101, 101, 103, 101, 104, 104, 100, 101 \} \rightarrow 12\)[/tex]
- For the interval [tex]\(105-109\)[/tex]: [tex]\( \{107, 109, 106 \} \rightarrow 3\)[/tex]
- For the interval [tex]\(110-114\)[/tex]: [tex]\( \{112, 111, 113, 111, 113, 112, 110 \} \rightarrow 7\)[/tex]
- For the interval [tex]\(115-119\)[/tex]: [tex]\( \{117, 117, 117, 117, 116, 116, 118, 117, 118, 115 \} \rightarrow 10\)[/tex]
Constructing the frequency distribution table, we have:
[tex]\[
\begin{tabular}{|c|c|}
\hline
Class Interval & Frequency \\
\hline
85-89 & 9 \\
\hline
90-94 & 4 \\
\hline
95-99 & 5 \\
\hline
100-104 & 12 \\
\hline
105-109 & 3 \\
\hline
110-114 & 7 \\
\hline
115-119 & 10 \\
\hline
\end{tabular}
\][/tex]
Thus, the grouped frequency distribution for the given IQ scores is:
[tex]\[
\begin{array}{|c|c|c|}
\hline
Class Interval & Frequency \\
\hline
85-89 & 9 \\
\hline
90-94 & 4 \\
\hline
95-99 & 5 \\
\hline
100-104 & 12 \\
\hline
105-109 & 3 \\
\hline
110-114 & 7 \\
\hline
115-119 & 10 \\
\hline
\end{array}
\][/tex]
