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Chapter 3: Problem 15

The following table is from a sample of five hundred homes in Oregon that were asked the primary source of heating in their home. a. How many of the households heat their home with firewood? b. What percent of households heat their home with natural gas? $$ \begin{array}{|c|c|} \hline \text { Type of Heat } & \text { Relative Frequency (\%) } \\ \hline \text { Electricity } & 33 \\ \hline \text { Heating Oil } & 4 \\ \hline \text { Natural Gas } & 50 \\ \hline \text { Firewood } & 8 \\ \hline \text { Other } & 5 \\ \hline \end{array} $$

Short Answer

Expert verified
40 households use firewood; 50% of households use natural gas.

Step by step solution

01

Identify Relative Frequency for Firewood

Look at the relative frequency table given for the different sources of heat. Find the percentage that corresponds to firewood. According to the table, the relative frequency for firewood is 8%.
02

Calculate Number of Households using Firewood

To find out how many households use firewood, convert the percentage into an actual count. Since the total number of households surveyed is 500, calculate 8% of 500. Use the formula: \( \text{Number of Households} = \frac{8}{100} \times 500 \).
03

Perform Calculation for Firewood Households

Now perform the multiplication: \( \frac{8}{100} \times 500 = 40 \). This means 40 households use firewood as their primary source of heating.
04

Identify Relative Frequency for Natural Gas

Look back at the relative frequency table to find the percentage of households that use natural gas. According to the table, the percentage for natural gas is 50%.
05

State Percentage for Natural Gas

The percentage of households that heat their home with natural gas is directly obtained from the chart, which is 50%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Relative Frequency
Relative frequency is a way to describe how often something happens compared to all possible outcomes. In the household survey, each type of heating source is represented as a percentage of the total number of surveyed homes. This method provides a clear picture of how common each heating option is within the sample.
For example, if firewood has a relative frequency of 8%, this means that 8 out of every 100 homes use firewood for heating. It鈥檚 an easy way to translate survey data into understandable chunks of information. When analyzing a relative frequency chart, you simply look at the percentage next to each category to understand its significance within the whole sample.
This type of frequency measure is particularly helpful in surveys as it shows direct proportional representations of data.
Percent Calculation
Calculating percentages from given data is a common task in statistics, often used in surveys to provide usable insights. For any given percentage in the survey, you can convert this to a number of households. This requires multiplying the total number of survey subjects by the percentage in question.
Here鈥檚 a quick step-by-step guide to perform such calculations:
  • Take the percentage value of interest.
  • Convert it into a decimal by dividing by 100.
  • Multiply this decimal by the total number of households surveyed.

For instance, to calculate how many households use firewood: Use the formula, \( \frac{8}{100} \times 500 \), which results in 40 households. This method ensures you are translating percentages back into meaningful counts that can be better understood in real-world contexts.
Household Survey
A household survey is a method of data collection focused on collecting information from a sample group of households. In our example, the survey collected data from 500 households in Oregon to determine their primary heating sources.
This type of survey is crucial in gathering data that can reveal consumer preferences, behaviors, and trends at a local or even national level. Surveys like this inform everything from market research to public policy as they provide snapshot insights into particular aspects of household living.
Some key benefits of household surveys include:
  • Large amounts of data can be gathered relatively quickly and cost-effectively.
  • They provide rich, varied data that can be used to make informed decisions.
  • These surveys can be targeted to specific geographic or demographic groups.
Household surveys effectively capture the diversity and complexity of domestic living arrangements.

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Most popular questions from this chapter

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