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Ch. 2 - Acute Angles and Right Triangles
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook
All textbooksLial 12th EditionCh. 2 - Acute Angles and Right TrianglesProblem 10
Chapter 3, Problem 10

Concept Check Refer to the discussion of accuracy and significant digits in this section to answer the following. WNBA Scorer Women's National Basketball Association player Breanna Stewart of the Seattle Storm was the WNBA's top scorer for the 2018 regular season, with 742 points. Is it appropriate to consider this number between 741.5 and 742.5? Why or why not? (Data from www.wnba.com)

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1
Understand the concept of significant digits and accuracy: When a number is reported as 742 points, it implies a certain level of precision, typically meaning the value is accurate to the nearest whole number.
Consider the meaning of the range 741.5 to 742.5: This range represents all values that would round to 742 when rounded to the nearest whole number.
Determine if the original number 742 can be considered within this range: Since 742 is rounded to the nearest whole number, it is appropriate to say the actual value lies somewhere between 741.5 and 742.5, assuming the data is rounded and not exact.
Reflect on the context of the data: In sports statistics, points are counted as whole numbers, so the value 742 is exact rather than an approximation, meaning it is not just an estimate within a range but a precise count.
Conclude whether it is appropriate to consider 742 between 741.5 and 742.5: Because the points are exact counts, it is not appropriate to treat 742 as an approximate value within that range; it should be considered an exact integer.

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Key Concepts

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

Significant Digits and Rounding

Significant digits represent the precision of a measured or reported number. When rounding to a certain number of significant digits, the value is approximated within a range, typically ±0.5 of the last digit. Understanding this helps determine if a number like 742 can be considered between 741.5 and 742.5.
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Measurement Accuracy and Precision

Accuracy refers to how close a reported number is to the true value, while precision indicates the consistency or exactness of the measurement. In sports statistics, reported totals are often exact counts, not estimates, affecting whether ranges around the number are meaningful.
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Context of Data Reporting

The nature of the data—whether it is a counted total or a measured estimate—affects interpretation. Since points scored are discrete counts, the number 742 is exact, making it inappropriate to consider it as a range between 741.5 and 742.5, which applies more to measured values.
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