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K Diameters of Golf Balls 1.35 1.62 1.32 1.52 1.59 1.65 1.48 1.65 1.49 1.62 1.48 1.65 1.67 1.48 1.61 Copy D

K Diameters of Golf Balls 1.35 1.62 1.32 1.52 1.59 1.65 1.48 1.65 1.49 1.62 1.48 1.65 1.67 1.48 1.61 Copy D

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Understanding Percentiles with Golf Ball Diameters** **Problem Statement:** Given the following data, find the diameter that represents the 36th percentile. **Data Table:** | Diameters of Golf Balls | |-------------------------| | 1.35 | 1.62 | 1.32 | 1.52 | 1.59 | | 1.65 | 1.48 | 1.65 | 1.49 | 1.62 | | 1.48 | 1.65 | 1.67 | 1.48 | 1.61 | **Explanation:** To find the 36th percentile, follow these steps: 1. **Arrange the Data**: Organize the golf ball diameters in ascending order. 2. **Calculate the Index**: Use the formula \( P \times N \) where \( P \) is the percentile in decimal (0.36 for the 36th percentile) and \( N \) is the total number of data points. 3. **Find the Diameter**: Use the index to determine which diameter represents the 36th percentile. **Step-by-Step Solution:** 1. **Organize the Data**: - Arrange all the given diameters in increasing order. 2. **Calculate the Index**: - Let \( N = \) total number of diameters. - \( N = 15 \) (3 rows, 5 columns). - Index = \( 0.36 \times 15 = 5.4 \). 3. **Determine the Diameter**: - A non-whole index suggests averaging: - Find the 5th and 6th values in the sorted list. - Average them to find the precise value for the 36th percentile. **Final Answer**: The 36th percentile corresponds to a diameter of approximately 1.48 (based on the dataset and calculations).
Transcribed Image Text:**Understanding Percentiles with Golf Ball Diameters** **Problem Statement:** Given the following data, find the diameter that represents the 36th percentile. **Data Table:** | Diameters of Golf Balls | |-------------------------| | 1.35 | 1.62 | 1.32 | 1.52 | 1.59 | | 1.65 | 1.48 | 1.65 | 1.49 | 1.62 | | 1.48 | 1.65 | 1.67 | 1.48 | 1.61 | **Explanation:** To find the 36th percentile, follow these steps: 1. **Arrange the Data**: Organize the golf ball diameters in ascending order. 2. **Calculate the Index**: Use the formula \( P \times N \) where \( P \) is the percentile in decimal (0.36 for the 36th percentile) and \( N \) is the total number of data points. 3. **Find the Diameter**: Use the index to determine which diameter represents the 36th percentile. **Step-by-Step Solution:** 1. **Organize the Data**: - Arrange all the given diameters in increasing order. 2. **Calculate the Index**: - Let \( N = \) total number of diameters. - \( N = 15 \) (3 rows, 5 columns). - Index = \( 0.36 \times 15 = 5.4 \). 3. **Determine the Diameter**: - A non-whole index suggests averaging: - Find the 5th and 6th values in the sorted list. - Average them to find the precise value for the 36th percentile. **Final Answer**: The 36th percentile corresponds to a diameter of approximately 1.48 (based on the dataset and calculations).
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