2. Describing Data with Tables and Graphs
Frequency Distributions
1:30 minutesProblem 2.5.32
Textbook Question
Interpreting Percentiles In Exercises 29–32, use the ogive, which represents the cumulative frequency distribution for quantitative reasoning scores on the Graduate Record Examination in a recent range of years. (Adapted from Educational Testing Service)
What percentile is a score of 170? How should you interpret this?
Verified step by step guidance1
Step 1: Understand the ogive graph. An ogive is a cumulative frequency graph that shows the percentage of data points below a certain value. The x-axis represents the scores, and the y-axis represents the percentiles.
Step 2: Locate the score of 170 on the x-axis of the graph. Draw a vertical line from this point upward until it intersects the curve.
Step 3: From the point of intersection, draw a horizontal line to the y-axis. This will give the corresponding percentile for the score of 170.
Step 4: Interpret the percentile value. The percentile indicates the percentage of test-takers who scored below 170. For example, if the percentile is 95, it means 95% of test-takers scored below 170.
Step 5: Use this information to understand the relative performance. A high percentile (e.g., 95th) suggests that the score of 170 is better than most test-takers, placing the individual in the top 5%.
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