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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 2.3.62c
Chapter 2, Problem 2.3.62c

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


c. Compare the measures you found in part (b) with those found in part (a). What do you notice?

Verified step by step guidance
1
Step 1: Understand the problem. In part (a), you likely calculated measures of central tendency (mean, median, mode) and measures of spread (range, variance, standard deviation) for the given data. In part (b), you may have calculated similar measures for a different dataset or subset of the data. The goal in part (c) is to compare these measures from part (a) and part (b).
Step 2: Review the measures of central tendency (mean, median, mode) from part (a) and part (b). Compare how these values differ between the two datasets. For example, check if the mean or median is higher or lower in one dataset compared to the other.
Step 3: Examine the measures of spread (range, variance, standard deviation) from part (a) and part (b). Determine if one dataset has a greater spread or variability than the other. For instance, a higher standard deviation indicates more variability in the data.
Step 4: Consider the context of the data. Reflect on why the measures might differ between the two datasets. For example, if part (b) involved a subset of the data (e.g., only par-3 holes), the measures might naturally differ due to the characteristics of that subset.
Step 5: Summarize your observations. Clearly state the differences and similarities you notice between the measures from part (a) and part (b). Highlight any patterns or insights that emerge from the comparison.

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Key Concepts

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

Measures of Central Tendency

Measures of central tendency, including mean, median, and mode, summarize a set of data points by identifying the center of the distribution. The mean is the average, calculated by summing all values and dividing by the count. The median is the middle value when data is ordered, while the mode is the most frequently occurring value. Understanding these measures helps in comparing different data sets effectively.
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Calculating the Mean

Measures of Dispersion

Measures of dispersion, such as range, variance, and standard deviation, describe the spread or variability of a data set. The range is the difference between the maximum and minimum values, while variance and standard deviation quantify how much individual data points differ from the mean. These measures are crucial for understanding the consistency and reliability of the data, especially when comparing different sets.
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Data Comparison

Data comparison involves analyzing two or more sets of data to identify similarities, differences, and trends. This can include comparing measures of central tendency and dispersion to assess how the data sets relate to each other. In the context of the golf course distances, comparing the results from parts (a) and (b) will reveal insights about the distribution and characteristics of the holes, such as whether they are generally longer or shorter.
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Related Practice
Textbook Question

Graphical Analysis In Exercises 21–24, you are asked to compare three data sets.


(c) Estimate the sample standard deviations. Then determine how close each of your estimates is by finding the sample standard deviations.


i.

ii.

iii.

Textbook Question

Shifting Data Sample annual salaries (in thousands of dollars) for employees at a company are listed.

40   35   49   53   38   39   40

37   49   34   38   43   47   35


c. Each employee in the sample takes a pay cut of \$2000 from their original salary. Find the sample mean and the sample standard deviation for the revised data set.

Textbook Question

Use the data set and the indicated number of classes to construct


(c) a frequency polygon,

Pulse Rates

Number of classes: 6 Data set: Pulse rates of all students in a class 68 105 95 80 90 100 75 70 84 98 102 70 65 88 90 75 78 94 110 120 95 80 76 108

Textbook Question

Mean Absolute Deviation Another useful measure of variation for a data set is the mean absolute deviation (MAD). It is calculated by the formula

MAD = Σ |x − x̄| / n.

b. Find the mean absolute deviation of the data set in Exercise 16. Compare your result with the sample standard deviation obtained in Exercise 16.

Textbook Question

Life Spans of Tires A brand of automobile tire has a mean life span of 35,000 miles, with a standard deviation of 2250 miles. Assume the life spans of the tires have a bell-shaped distribution.


b. The life spans of three randomly selected tires are 30,500 miles, 37,250 miles, and 35,000 miles. Using the Empirical Rule, find the percentile that corresponds to each life span.

Textbook Question

Extending Concepts


Trimmed Mean To find the 10% trimmed mean of a data set, order the data, delete the lowest 10% of the entries and the highest 10% of the entries, and find the mean of the remaining entries.


c. What is the benefit of using a trimmed mean versus using a mean found using all data entries? Explain your reasoning.