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What is the difference between the mean and the median of the set {10 12, 10, 16}? 01 01 04

What is the difference between the mean and the median of the set {10 12, 10, 16}? 01 01 04

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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### Mean vs. Median: Understanding the Difference **Question:** What is the difference between the mean and the median of the set \{10, 12, 10, 16\}? **Options:** - \( \circ \) 1 - \( \circ \) 1 - \( \circ \) 4 - \( \circ \) 9 - \( \circ \) 12 **Explanation:** To answer this question, we need to calculate both the mean and the median of the set and then find the difference between them. 1. **Mean (Average):** - Add all the numbers in the set: \( 10 + 12 + 10 + 16 = 48 \) - Divide the sum by the number of elements: \( 48 \div 4 = 12 \) - So, the mean of the set is \( 12 \). 2. **Median (Middle Value):** - Arrange the numbers in ascending order: \( 10, 10, 12, 16 \). - Since the number of elements is even (4), the median is the average of the two middle numbers. - The two middle numbers are \( 10 \) and \( 12 \). - Calculate the average of these two numbers: \( (10 + 12) \div 2 = 11 \). - So, the median of the set is \( 11 \). 3. **Difference:** - Subtract the median from the mean: \( 12 - 11 = 1 \). Thus, the correct answer is \( \circ 1 \).
Transcribed Image Text:### Mean vs. Median: Understanding the Difference **Question:** What is the difference between the mean and the median of the set \{10, 12, 10, 16\}? **Options:** - \( \circ \) 1 - \( \circ \) 1 - \( \circ \) 4 - \( \circ \) 9 - \( \circ \) 12 **Explanation:** To answer this question, we need to calculate both the mean and the median of the set and then find the difference between them. 1. **Mean (Average):** - Add all the numbers in the set: \( 10 + 12 + 10 + 16 = 48 \) - Divide the sum by the number of elements: \( 48 \div 4 = 12 \) - So, the mean of the set is \( 12 \). 2. **Median (Middle Value):** - Arrange the numbers in ascending order: \( 10, 10, 12, 16 \). - Since the number of elements is even (4), the median is the average of the two middle numbers. - The two middle numbers are \( 10 \) and \( 12 \). - Calculate the average of these two numbers: \( (10 + 12) \div 2 = 11 \). - So, the median of the set is \( 11 \). 3. **Difference:** - Subtract the median from the mean: \( 12 - 11 = 1 \). Thus, the correct answer is \( \circ 1 \).
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