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Statistics and Probability - Response rates

Grade 10IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The Response Rate is the ratio of the number of people who participated in a survey to the total number of people who were invited to participate.

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A high response rate is desirable because it increases the likelihood that the sample is representative of the entire population.

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A low response rate can lead to non-response bias, where the results are skewed because the people who chose not to respond may have different opinions or characteristics than those who did respond.

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Response rates are expressed as a percentage (%).

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Factors that can improve response rates include keepings surveys short, offering incentives, and sending follow-up reminders.

📐Formulae

Response Rate=Number of ResponsesTotal Number of Surveys Distributed×100%\text{Response Rate} = \frac{\text{Number of Responses}}{\text{Total Number of Surveys Distributed}} \times 100\%

Total Surveys Distributed=Number of ResponsesResponse Rate (as a decimal)\text{Total Surveys Distributed} = \frac{\text{Number of Responses}}{\text{Response Rate (as a decimal)}}

💡Examples

Problem 1:

A researcher sends out 400400 email surveys to students to gather data on their study habits. By the end of the week, 112112 students have completed the survey. Calculate the response rate.

Solution:

Response Rate=112400×100=28%\text{Response Rate} = \frac{112}{400} \times 100 = 28\%

Explanation:

To find the response rate, divide the number of successful responses (112112) by the total number of surveys sent (400400), then multiply by 100100 to convert the fraction into a percentage.

Problem 2:

A local council wants to achieve a 45%45\% response rate for their new community project survey. If they need at least 270270 responses to make the data statistically significant, how many surveys should they distribute at minimum?

Solution:

0.45×x=2700.45 \times x = 270 x=2700.45x = \frac{270}{0.45} x=600x = 600

Explanation:

We use the relationship Responses=Total×Rate\text{Responses} = \text{Total} \times \text{Rate}. Rearranging to find the total, we divide the required responses (270270) by the target rate expressed as a decimal (0.450.45). They need to distribute 600600 surveys.

Problem 3:

In a survey about school lunches, 800800 questionnaires were handed out. 340340 were returned. Calculate the number of non-respondents and use it to find the percentage of people who did NOT respond.

Solution:

800−340460\begin{array}{r} 800 \\ -340 \\ \hline 460 \end{array} Non-response Rate=460800×100=57.5%\text{Non-response Rate} = \frac{460}{800} \times 100 = 57.5\%

Explanation:

First, subtract the number of responses from the total to find the non-respondents (460460). Then, divide this by the total (800800) and multiply by 100100 to get the non-response rate of 57.5%57.5\%.