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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
All textbooksLarson 8th EditionCh. 2 - Descriptive StatisticsProblem 2.1.46c
Chapter 2, Problem 2.1.46c

What Would You Do? The admissions department for a college is asked to recommend the minimum SAT scores that the college will accept for full-time students. The SAT scores of 50 applicants are listed. 1170 1000 910 870 1070 1290 920 1470 1080 1180 770 900 1120 1070 1370 1160 970 930 1240 1270 1250 1330 1010 1010 1410 1130 1210 1240 960 820 650 1010 1190 1500 1400 1270 1310 1050 950 1150 1450 1290 1310 1100 1330 1410 840 1040 1090 1080
If you want to accept the top 88% of the applicants, what should the minimum score be? Explain.

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Step 1: Organize the data. Start by listing all the SAT scores in ascending order. This will help in identifying the percentile ranks of the scores.
Step 2: Determine the percentile rank corresponding to the top 88% of applicants. The top 88% means that 12% of the applicants will be excluded. Calculate the position in the sorted list that corresponds to the 12th percentile using the formula: Position = (P/100) * (N + 1), where P is the percentile (12 in this case) and N is the total number of applicants (50).
Step 3: Locate the score at the calculated position. If the position is not an integer, interpolate between the two closest scores in the sorted list to find the exact value.
Step 4: Interpret the result. The score at the 12th percentile represents the minimum SAT score required to accept the top 88% of applicants.
Step 5: Conclude by explaining that this score will serve as the cutoff for admissions, ensuring that only the top 88% of applicants are accepted based on their SAT scores.

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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 measure used in statistics to indicate the value below which a given percentage of observations fall. For example, the 88th percentile means that 88% of the data points are below this value. In the context of the SAT scores, determining the 88th percentile will help identify the minimum score that separates the top 12% of applicants from the rest.

Descriptive Statistics

Descriptive statistics summarize and describe the main features of a dataset. This includes measures such as mean, median, mode, and range. In this scenario, understanding how to calculate and interpret these statistics is essential for analyzing the SAT scores and determining the cutoff score for the top 88% of applicants.
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Data Sorting

Data sorting involves arranging data in a specific order, typically ascending or descending. For this question, sorting the SAT scores from lowest to highest is crucial to easily identify the score that corresponds to the 88th percentile. This process allows for a clear visualization of where the cutoff lies among the applicants' scores.
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