The following data represent the number of potholes on 35 randomly selected 1-mile stretches of highway around a particular city. Complete parts (a) through (g) below.
\begin{tabular}{ccccc}
\multicolumn{5}{c}{ Number of Potholes } \\
\hline 1 & 4 & 3 & 1 & 3 \\
4 & 5 & 1 & 3 & 6 \\
1 & 2 & 2 & 1 & 2 \\
7 & 1 & 6 & 2 & 7 \\
1 & 6 & 4 & 4 & 1 \\
1 & 5 & 3 & 6 & 2 \\
3 & 2 & 7 & 1 & 3
\end{tabular}
(a) Construct a frequency distribution of the data.
\begin{tabular}{|c|c|}
\hline Potholes & Frequency \\
\hline 1 & $\square$ \\
2 & $\square$ \\
3 & $\square$ \\
4 & $\square$ \\
5 & $\square$ \\
6 & $\square$ \\
7 & $\square$ \\
\hline
\end{tabular}
Answer (2)
Count the occurrences of each number of potholes (1 to 7) in the dataset.
Record the frequencies for each number: 1 (10 times), 2 (6 times), 3 (6 times), 4 (4 times), 5 (2 times), 6 (4 times), 7 (3 times).
Create a frequency distribution table with 'Potholes' and 'Frequency' columns.
Populate the table with the corresponding frequencies: See table in step 5 .
Explanation
Understand the problem and provided data We are given a set of data representing the number of potholes on 35 different 1-mile stretches of highway. Our task is to organize this data into a frequency distribution table, which will show how many times each number of potholes appears in the dataset. This will help us understand the distribution of potholes across the sampled highway stretches.
Determine the frequency of each number of potholes To construct the frequency distribution, we need to count how many times each number from 1 to 7 appears in the dataset. The numbers represent the number of potholes found on a 1-mile stretch of highway. We will count the occurrences of each number and record it as the frequency.
Count the occurrences of each number Based on the provided data, the frequencies for each number of potholes are as follows:
The number 1 appears 10 times.
The number 2 appears 6 times.
The number 3 appears 6 times.
The number 4 appears 4 times.
The number 5 appears 2 times.
The number 6 appears 4 times.
The number 7 appears 3 times.
Construct the frequency distribution table Now, we can create the frequency distribution table using the counts we just determined. The table will have two columns: 'Potholes' and 'Frequency'. The 'Potholes' column will list the numbers from 1 to 7, and the 'Frequency' column will show how many times each number appears in the dataset.
Present the final frequency distribution table The completed frequency distribution table is:
Potholes
Frequency
1
10
2
6
3
6
4
4
5
2
6
4
7
3
Examples
Understanding the frequency of potholes on roads can help city planners allocate resources effectively. For example, if a frequency distribution shows that a particular area has a high number of potholes, the city can prioritize road maintenance and repair in that area. This data-driven approach ensures that resources are used where they are most needed, improving road conditions and safety for drivers. By analyzing the frequency of different issues, cities can make informed decisions about infrastructure management and budget allocation.
To create a frequency distribution of potholes from the dataset, we counted the occurrences of each number of potholes. The resulting table shows how many times each count appears, with 10 occurrences of 1, 6 of 2, and so on. This organization helps in understanding the distribution and prevalence of potholes across the sampled highway stretches.
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