An electronics company polled 300 random people to find out whether they own cell phones and laptops. The results are shown in the table.
\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 } \multicolumn{1}{c|}{} & \begin{tabular}{c} Cell \\
Phone \end{tabular} & \begin{tabular}{c} No Cell \\
Phone \end{tabular} & Total \\
\hline Laptop & 82 & 11 & $b$ \\
\hline \begin{tabular}{c} No \\
Laptop \end{tabular} & 159 & $a$ & 207 \\
\hline Total & 241 & 59 & 300 \\
\hline
\end{tabular}
Use the table to complete the statements.
The cell labeled $a$ is a $\square$
The cell labeled $b$ is $a$ $\square$
Answer (1)
Calculate the value of 'a' by subtracting the number of people who own a laptop and do not own a cell phone (11) from the total number of people who do not own a cell phone (59): a = 59 − 11 = 48 .
Calculate the value of 'b' by adding the number of people who own a cell phone and a laptop (82) and the number of people who own a laptop and do not own a cell phone (11): b = 82 + 11 = 93 .
Alternatively, calculate the value of 'b' by subtracting the number of people who do not own a laptop (207) from the total number of people surveyed (300): b = 300 − 207 = 93 .
The cell labeled a is 48 and the cell labeled b is a 45 more than.
Explanation
Understand the problem and provided data We are given a table representing the results of a survey about cell phone and laptop ownership. Our goal is to find the values of cells 'a' and 'b' in the table. Cell 'a' represents the number of people who do not own a laptop and do not own a cell phone. Cell 'b' represents the total number of people who own a laptop.
Calculate the value of a To find the value of 'a', we can use the information that the total number of people who do not own a cell phone is 59. Of these 59 people, 11 own a laptop. Therefore, the number of people who do not own a laptop and do not own a cell phone is the difference between the total number of people who do not own a cell phone and the number of people who own a laptop but do not own a cell phone. Thus, a = 59 − 11 = 48
Calculate the value of b To find the value of 'b', we can use the information that 'b' represents the total number of people who own a laptop. We know that 82 people own both a cell phone and a laptop, and 11 people own a laptop but do not own a cell phone. Therefore, the total number of people who own a laptop is the sum of these two numbers. Thus, b = 82 + 11 = 93
Alternative calculation of b Alternatively, we know that the total number of people surveyed is 300, and 207 people do not own a laptop. Therefore, the number of people who own a laptop is the difference between the total number of people surveyed and the number of people who do not own a laptop. Thus, b = 300 − 207 = 93
Final Answer The cell labeled a is 48. The cell labeled b is a 45 more than.
Examples
Understanding surveys and data tables is crucial in many real-world scenarios, from market research to social science. For example, a company might use a survey to understand how many people in a specific demographic own their product versus a competitor's. This information helps them tailor their marketing strategies and product development to better meet customer needs. Similarly, political campaigns use surveys to gauge voter sentiment and adjust their messaging accordingly. Knowing how to interpret and complete these tables is a fundamental skill in data analysis.
