2. Describing Data with Tables and Graphs
Frequency Distributions
3:38 minutesProblem 2.1.22
Textbook Question
Analysis of Last Digits Weights of respondents were recorded as part of the California Health Interview Survey. The last digits of weights from 50 randomly selected respondents are listed below. Construct a frequency distribution with 10 classes. Based on the distribution, do the weights appear to be reported or actually measured? Does there appear to be a gap in the frequencies and, if so, how might that gap be explained? What do you know about the accuracy of the results?
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Step 1: Extract the last digits from the provided data. These digits are already listed in the image, so you can directly use them for analysis.
Step 2: Construct a frequency distribution with 10 classes. Each class corresponds to a single digit (0 through 9). Count the occurrences of each digit in the data set.
Step 3: Create a table or chart to represent the frequency distribution. For example, list each digit (0-9) in one column and its frequency in the adjacent column.
Step 4: Analyze the frequency distribution to determine if the weights appear to be reported or measured. If certain digits (e.g., 0 or 5) occur disproportionately, it may suggest that the weights were rounded or reported rather than precisely measured.
Step 5: Examine the accuracy of the results and identify any gaps in the frequencies. If there is a noticeable gap or clustering around specific digits, it could indicate rounding or estimation. Discuss how this might affect the reliability of the data.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Frequency Distribution
A frequency distribution is a summary of how often each value occurs in a dataset. It organizes data into classes or intervals, allowing for easier analysis of patterns and trends. In this case, constructing a frequency distribution with 10 classes will help visualize the distribution of the last digits of weights, revealing any potential biases or anomalies in the data.
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Reported vs. Measured Data
Reported data refers to values that individuals provide, which may be influenced by rounding or personal bias, while measured data is obtained through precise instruments. Analyzing the frequency distribution can help determine if the last digits of weights appear random (suggesting measurement) or exhibit patterns (indicating reporting), which can affect the reliability of the data.
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Gaps in Frequencies
Gaps in frequencies within a distribution can indicate irregularities or biases in data collection. For instance, if certain last digits are underrepresented, it may suggest that respondents rounded their weights to the nearest ten or avoided reporting certain numbers. Understanding these gaps is crucial for assessing the accuracy and validity of the survey results.
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