3. Describing Data Numerically

Median

3. Describing Data Numerically

Median

2:24 minutes

Problem 2.3.62d

Textbook Question

Extending Concepts

Golf The distances (in yards) for nine holes of a golf course are listed.
336 393 408 522 147 504 177 375 360

d. Use your results from part (c) to explain how to quickly find the mean and the median of the original data set when the distances are converted to inches.

Verified step by step guidance

Step 1: Recall the conversion factor between yards and inches. Since 1 yard equals 36 inches, any distance in yards can be converted to inches by multiplying it by 36.

Step 2: To find the mean of the original data set in inches, note that the mean of a data set is the sum of all values divided by the number of values. When converting the distances to inches, each value is multiplied by 36. Therefore, the mean in inches can be calculated by multiplying the mean in yards by 36.

Step 3: To find the median of the original data set in inches, recall that the median is the middle value when the data is ordered. Since converting to inches involves multiplying each value by 36, the relative order of the data does not change. Thus, the median in inches is simply the median in yards multiplied by 36.

Step 4: Summarize the key insight: When converting a data set from one unit to another by multiplying by a constant, both the mean and the median are scaled by the same constant. This allows for quick computation without recalculating from scratch.

Step 5: Apply this understanding to the given data set. Use the mean and median from part (c) (in yards) and multiply each by 36 to find the mean and median in inches.

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Key Concepts

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

Mean

The mean, or average, is calculated by summing all values in a data set and dividing by the number of values. In this case, to find the mean of the golf hole distances in inches, you would first convert each distance from yards to inches (1 yard = 36 inches), sum these converted values, and then divide by the total number of holes.

Median

The median is the middle value of a data set when arranged in ascending order. If the number of observations is odd, the median is the middle number; if even, it is the average of the two middle numbers. For the golf distances converted to inches, you would first convert the values, sort them, and then identify the median based on their position in the ordered list.

Unit Conversion

Unit conversion involves changing a measurement from one unit to another, which is essential when comparing or analyzing data in different units. In this scenario, converting the golf hole distances from yards to inches is necessary to maintain consistency in measurement, ensuring that calculations for mean and median are accurate and meaningful.

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Textbook Question

Protein Powder During a quality assurance check, the actual contents (in grams) of six containers of protein powder were recorded as 1525, 1526, 1502, 1516, 1529, and 1511.

a. Find the mean and the median of the contents.

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Textbook Question

U.S. Trade Deficits The table at the left shows the U.S. trade deficits (in billions of dollars) with 18 countries in 2020. (Source: U.S. Department of Commerce)

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a. Find the mean and the median of the trade deficits.

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Textbook Question

The overall averages of 12 students in a statistics class prior to taking the final exam are listed.

67 72 88 73 99 85 81 87 63 94 68 87

a. Find the mean, median, and mode of the data set. Which best represents the center of the data?

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Textbook Question

Extending Concepts

Golf The distances (in yards) for nine holes of a golf course are listed.

336 393 408 522 147 504 177 375 360

a. Find the mean and the median of the data.

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Textbook Question

Extending Concepts

Data Analysis Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are shown in the table at the left.

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a. Find the mean and the median of the data.

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Textbook Question

In Exercises 13 and 14, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why.

The responses of 1019 adults who were asked how much money they think they will spend on Christmas gifts in a recent year (Adapted from Gallup)

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Multiple Choice

Find the median of the sample data below.

Resistant Measures Listed below are 10 wait times (minutes) for “Rock ‘n’ Roller Coaster” at 10 AM (from Data Set 33 “Disney World Wait Times”). The data are listed in order from lowest to highest. Find the mean and median of these ten values. Then find the mean and median after excluding the value of 180, which appears to be an outlier. Compare the two sets of results. How much was the mean affected by the inclusion of the outlier? How much is the median affected by the inclusion of the outlier?

15 20 25 30 30 35 45 50 50 180

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Show more practices

Extending ConceptsGolf The distances (in yards) for nine holes of a golf course are listed.336 393 408 522 147 504 177 375 360d. Use your results from part (c) to explain how to quickly find the mean and the median of the original data set when the distances are converted to inches.

Key Concepts

Mean

Median

Unit Conversion

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Extending Concepts

Golf The distances (in yards) for nine holes of a golf course are listed.
336 393 408 522 147 504 177 375 360

d. Use your results from part (c) to explain how to quickly find the mean and the median of the original data set when the distances are converted to inches.