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Diagnose why Dr. Aris's initial standard frequency table failed to summarize the reaction time data effectively. Explain how converting the data into a grouped frequency table resolves this issue, and justify the structural layout Dr. Aris should use for the new table, referencing the recommended number and width style of the intervals.
Case context: Dr. Aris is analyzing reaction times from a cognitive psychology study involving participants. The reaction times range widely from ms to ms, with almost every participant having a unique score. Dr. Aris initially creates a standard frequency table listing every unique reaction time score in the first column, but finds that the table is cluttered, spans multiple pages, and fails to show any clear patterns in the data.
Question: Diagnose why Dr. Aris's initial standard frequency table failed to summarize the reaction time data effectively. Explain how converting the data into a grouped frequency table resolves this issue, and justify the structural layout Dr. Aris should use for the new table, referencing the recommended number and width style of the intervals.
Sample answer: The standard frequency table failed because the dataset has a broad range of scores with a large number of unique values. Listing each unique score results in a table nearly as long as the raw data, with frequencies of only or , which fails to summarize the data. A grouped frequency table solves this by displaying ranges of values instead of individual scores. Dr. Aris should structure the new table with two columns: the first column displaying between and equal-width intervals of reaction times, and the second column displaying the frequency of scores in each interval. This condenses the broad range into a concise, readable format that reveals the distribution pattern.
Key points:
- A standard frequency table is ineffective when there is a broad range of many unique scores because it does not summarize the data.
- A grouped frequency table summarizes data by displaying ranges of values in the first column.
- The first column must use equal-width intervals.
- The number of intervals should typically be between and .
- The second column must show the frequency of scores falling into each range.
Rubric: The response must explain: 1. That a standard frequency table fails to summarize data when there is a broad range of many different unique scores. 2. That a grouped frequency table resolves this by grouping individual scores into ranges of values. 3. The layout: the first column displays ranges of values and the second column displays the frequency of scores. 4. The interval rules: the table must use equal-width intervals, typically numbering between and .
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Grouped Frequency Table of Reaction Times
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