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Thirty-two people were chosen at random from employees of a large company. Their commute times (in hours) were recorded in a table (shown below).

\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
0.5 & 0.9 & 0.5 & 0.4 & 0.7 & 1.3 & 1.0 & 0.7 \\
\hline
0.6 & 0.4 & 0.8 & 1.0 & 0.9 & 1.4 & 0.4 & 1.1 \\
\hline
0.9 & 1.1 & 0.7 & 0.2 & 0.6 & 1.0 & 0.7 & 1.2 \\
\hline
0.4 & 1.2 & 0.7 & 0.6 & 1.3 & 0.8 & 0.4 & 0.9 \\
\hline
\end{tabular}

Construct a frequency table using a class interval width of 0.2 starting at 0.15.

(Type integers or simplified fractions.)

\begin{tabular}{|lll|}
\hline
Class Interval & Frequency & Relative Frequency \\
\hline
0.15-0.35 & & \\
0.35-0.55 & & \\
0.55-0.75 & & \\
0.75-0.95 & & \\
0.95-1.15 & & \\
1.15-1.35 & & \\
1.35-1.55 & & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Let’s construct the frequency table step by step.

1. Define the Class Intervals:
The problem specifies that the class interval width is 0.2 starting from 0.15. The class intervals will be:
- 0.15 - 0.35
- 0.35 - 0.55
- 0.55 - 0.75
- 0.75 - 0.95
- 0.95 - 1.15
- 1.15 - 1.35
- 1.35 - 1.55

2. Determine Frequencies for Each Class Interval:
We count how many commute times fall within each interval:
- 0.15 - 0.35:
- Commute times in this range: 0.2
- Frequency: 1

- 0.35 - 0.55:
- Commute times in this range: 0.4, 0.4, 0.4, 0.4, 0.5, 0.5, 0.4
- Frequency: 7

- 0.55 - 0.75:
- Commute times in this range: 0.6, 0.7, 0.7, 0.7, 0.6, 0.7, 0.6, 0.7
- Frequency: 8

- 0.75 - 0.95:
- Commute times in this range: 0.8, 0.9, 0.9, 0.8, 0.9, 0.8
- Frequency: 6

- 0.95 - 1.15:
- Commute times in this range: 1.0, 1.0, 1.0, 1.1, 1.1
- Frequency: 5

- 1.15 - 1.35:
- Commute times in this range: 1.2, 1.2, 1.3, 1.2
- Frequency: 4

- 1.35 - 1.55:
- Commute times in this range: 1.4
- Frequency: 1

3. Calculate the Relative Frequencies:
The relative frequency is the frequency divided by the total number of observations (32 in this case).

Using this:
- 0.15 - 0.35:
- Frequency: 1
- Relative Frequency: [tex]\( \frac{1}{32} = 0.03125 \)[/tex]
- 0.35 - 0.55:
- Frequency: 7
- Relative Frequency: [tex]\( \frac{7}{32} = 0.21875 \)[/tex]
- 0.55 - 0.75:
- Frequency: 8
- Relative Frequency: [tex]\( \frac{8}{32} = 0.25 \)[/tex]
- 0.75 - 0.95:
- Frequency: 6
- Relative Frequency: [tex]\( \frac{6}{32} = 0.1875 \)[/tex]
- 0.95 - 1.15:
- Frequency: 5
- Relative Frequency: [tex]\( \frac{5}{32} = 0.15625 \)[/tex]
- 1.15 - 1.35:
- Frequency: 4
- Relative Frequency: [tex]\( \frac{4}{32} = 0.125 \)[/tex]
- 1.35 - 1.55:
- Frequency: 1
- Relative Frequency: [tex]\( \frac{1}{32} = 0.03125 \)[/tex]

4. Summarize in the Frequency Table:

[tex]\[ \begin{array}{|c|c|c|} \hline \text{Class Interval} & \text{Frequency} & \text{Relative Frequency} \\ \hline 0.15-0.35 & 1 & 0.03125 \\ 0.35-0.55 & 7 & 0.21875 \\ 0.55-0.75 & 8 & 0.25 \\ 0.75-0.95 & 6 & 0.1875 \\ 0.95-1.15 & 5 & 0.15625 \\ 1.15-1.35 & 4 & 0.125 \\ 1.35-1.55 & 1 & 0.03125 \\ \hline \end{array} \][/tex]