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 guidance

1. 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.
2. 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.
3. 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.
4. 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.
5. 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%.

Key Concepts

Percentiles

A percentile is a statistical measure that indicates the value below which a given percentage of observations fall. For example, if a score is at the 70th percentile, it means that 70% of the scores are below that value. This concept is crucial for interpreting individual scores in the context of a larger dataset, such as standardized test results.

Ogive

An ogive is a graph that represents the cumulative frequency of a dataset. It is constructed by plotting the cumulative frequency against the upper boundaries of the classes. In the context of the question, the ogive allows us to visually determine the percentile rank of a specific score, such as 170, by locating it on the x-axis and reading the corresponding percentile on the y-axis.

Cumulative Frequency

Cumulative frequency is the running total of frequencies in a dataset, showing how many observations fall below a particular value. It is essential for understanding the distribution of scores and is used to create the ogive. By analyzing cumulative frequency, one can determine how a specific score compares to others in the dataset, aiding in the interpretation of percentiles.