To accurately represent the data in a histogram, you need to identify the key characteristics: the intervals (or bins) and the frequencies. Here is the given frequency table again:
[tex]\[
\begin{array}{|l|l|}
\hline \text{Number of Hours} & \text{Frequency} \\
\hline 0-9 & 1 \\
\hline 10-19 & 6 \\
\hline 20-29 & 15 \\
\hline 30-39 & 12 \\
\hline 40-49 & 2 \\
\hline 50-59 & 4 \\
\hline
\end{array}
\][/tex]
Let's now describe how this information can be represented in a histogram step-by-step:
1. Intervals/Bins: The number of hours per week are grouped into intervals. Here, the intervals are:
- 0-9 hours
- 10-19 hours
- 20-29 hours
- 30-39 hours
- 40-49 hours
- 50-59 hours
2. Frequencies: The frequency of each interval represents how many families fall into each interval:
- 0-9 hours: 1 family
- 10-19 hours: 6 families
- 20-29 hours: 15 families
- 30-39 hours: 12 families
- 40-49 hours: 2 families
- 50-59 hours: 4 families
3. Constructing the Histogram:
- The x-axis represents the intervals of hours per week.
- The y-axis represents the frequency of families.
- Each bar's height is determined by the frequency of each interval.
Visually, the histogram would be constructed as follows:
- A bar from 0-9 hours that reaches up to 1 on the y-axis.
- A bar from 10-19 hours that reaches up to 6 on the y-axis.
- A bar from 20-29 hours that reaches up to 15 on the y-axis.
- A bar from 30-39 hours that reaches up to 12 on the y-axis.
- A bar from 40-49 hours that reaches up to 2 on the y-axis.
- A bar from 50-59 hours that reaches up to 4 on the y-axis.
By analyzing these features, you can compare the histograms provided (option a, b, etc.) and select the one that matches the data accurately.
