Ch. 2 - Descriptive Statistics

Larson - Elementary Statistics: Picturing the World 8th Edition

Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook

Larson 8th Edition

Ch. 2 - Descriptive Statistics

Problem 2.5.29

Chapter 2, Problem 2.5.29

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 score represents the 65th percentile? How should you interpret this?

Verified step by step guidance

Step 1: Understand the concept of percentiles. The 65th percentile means that 65% of the scores are below this value, and 35% are above it.

Step 2: Locate the 65th percentile on the vertical axis (y-axis) of the ogive graph. This corresponds to the cumulative percentage of 65%.

Step 3: Draw a horizontal line from the 65th percentile on the y-axis until it intersects the curve of the ogive.

Step 4: From the point of intersection, draw a vertical line down to the horizontal axis (x-axis) to determine the corresponding score.

Step 5: Interpret the result. The score at the 65th percentile represents the value below which 65% of the test takers scored. This score can be used to understand relative performance in the quantitative reasoning section.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Percentiles

A percentile is a statistical measure that indicates the value below which a given percentage of observations fall. For example, the 65th percentile means that 65% of the scores are below this value. Understanding percentiles helps in interpreting how a specific score compares to the overall distribution of scores.

Ogive

An ogive is a graph that represents the cumulative frequency of a dataset. It allows for the visualization of how many data points fall below a certain value. In this context, the ogive helps to determine the score corresponding to a specific percentile, such as the 65th percentile, by showing the cumulative distribution of quantitative reasoning scores.

Cumulative Frequency

Cumulative frequency is the running total of frequencies up to a certain point in a dataset. It provides insight into the distribution of data by showing how many observations fall below a particular score. In the context of the question, it is essential for interpreting the ogive and understanding the score that represents the 65th percentile.

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Textbook Question

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Textbook Question

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32.70 31.12 25.87 15.06 23.12 30.62 19.85

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