Questions: Surveys are often conducted on the trends in digital platforms. The frequency table below summarizes the number of working computers in household for a simple random sample of 19 households. Find the five-number summary. Report the five-number summary in the following order: Min, Q1, Median (Q2), Q3, Max. Number of Computers, Frequency 0, 1 1, 2 2, 3 3, 7 4, 5 5, 1

Solution Steps

To find the five-number summary (Min, Q1, Median (Q2), Q3, Max) for the given frequency table, we need to:

1. Expand the frequency table into a list of individual data points.
2. Sort the list of data points.
3. Calculate the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values from the sorted list.

We start by expanding the frequency table into a list of individual data points. The frequency table is given as: \[ \begin{array}{|c|c|} \hline \text{Number of Computers} & \text{Frequency} \\ \hline 0 & 1 \\ \hline 1 & 2 \\ \hline 2 & 3 \\ \hline 3 & 7 \\ \hline 4 & 5 \\ \hline 5 & 1 \\ \hline \end{array} \] Expanding this table, we get the list: \[ [0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5] \]

Next, we sort the list of data points: \[ [0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5] \]

Using the sorted list, we calculate the five-number summary:

• Minimum (\(\text{Min}\)): The smallest value in the list is \(0\).
• First Quartile (\(Q1\)): The 25th percentile of the list is \(2.0\).
• Median (\(Q2\)): The 50th percentile (middle value) of the list is \(3.0\).
• Third Quartile (\(Q3\)): The 75th percentile of the list is \(4.0\).
• Maximum (\(\text{Max}\)): The largest value in the list is \(5\).

Final Answer