Question

In 2014, Clayton Kershaw of the Los Angeles Dodgers had the lowest earned-run average (ERA is the mean number of runs yielded per nine innings pitched) of any starting pitcher in the National League, with an ERA of 1.77. Also in $2014,$ Felix Hernandez of the Seattle Mariners had the lowest ERA of any starting pitcher in the American League with an ERA of $2.14 .$ In the National League, the mean ERA in 2014 was 3.430 and the standard deviation was $0.721 .$ In the American League, the mean ERA in 2014 was 3.598 and the standard deviation was $0.762 .$ Which player had the better year relative to his peers? Why?

Name: Problem 9, Chapter 3: Statistics Informed Decisions Using Data
Uploaded: 2023-05-04T14:52:38-08:00
Duration: 2 min 50 s
Channel: Clayton Schubring

    In 2014, Clayton Kershaw of the Los Angeles Dodgers had the lowest earned-run average (ERA is the mean number of runs yielded per nine innings pitched) of any starting pitcher in the National League, with an ERA of 1.77. Also in $2014,$ Felix Hernandez of the Seattle Mariners had the lowest ERA of any starting pitcher in the American League with an ERA of $2.14 .$ In the National League, the mean ERA in 2014 was 3.430 and the standard deviation was $0.721 .$ In the American League, the mean ERA in 2014 was 3.598 and the standard deviation was $0.762 .$ Which player had the better year relative to his peers? Why?

Statistics Informed Decisions Using Data

Michael Sullivan III 5th Edition

Chapter 3, Problem 9

Instant Answer

Solved by Expert Clayton Schubring

05/04/2023

Step 1

The z-score is a measure of how many standard deviations an element is from the mean. In this case, a lower z-score is better because a lower ERA is better. The formula for the z-score is: \[ z = \frac{x - \mu}{\sigma} \] where $x$ is the sample (the player's Show more…

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In 2014, Clayton Kershaw of the Los Angeles Dodgers had the lowest earned-run average (ERA is the mean number of runs yielded per nine innings pitched) of any starting pitcher in the National League, with an ERA of 1.77. Also in $2014,$ Felix Hernandez of the Seattle Mariners had the lowest ERA of any starting pitcher in the American League with an ERA of $2.14 .$ In the National League, the mean ERA in 2014 was 3.430 and the standard deviation was $0.721 .$ In the American League, the mean ERA in 2014 was 3.598 and the standard deviation was $0.762 .$ Which player had the better year relative to his peers? Why?

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Key Concepts

Z-Score

The z-score is a statistical measure that represents the number of standard deviations a specific value is from the mean. It standardizes different datasets, allowing for direct comparison of relative performance by showing how far an observation deviates from the typical value.

Standard Deviation

The standard deviation quantifies the amount of variation or dispersion in a set of values. It indicates how spread out the values are around the mean, offering insight into the consistency or variability of the dataset.

Mean

The mean is the arithmetic average of a set of values and is commonly used as a measure of central tendency in a dataset. It provides a reference point against which individual performances or measurements can be compared.

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