Answered: What meadure of variability would you…

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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Question

What meadure of variability would you use for a data set with a normal distribution?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1: prerequisites

1. Basic Arithmetic:

You should be comfortable with basic arithmetic operations such as addition, subtraction, multiplication, and division.

2. Understanding of Summation (Σ) Notation:

Knowledge of how to use the summation notation (Σ) is essential. It represents the sum of a sequence of numbers. For example, Σ(xi) means the sum of all individual data points.

3. Mean (Average) Calculation:

You need to know how to calculate the mean of a dataset. The mean is the sum of all data points divided by the total number of data points.

4. Squaring and Square Roots:

Understanding how to square a number (x²) and take the square root of a number (√x) is important, as these operations are involved in the standard deviation formula.

5. Understanding Variance:

While not strictly necessary for understanding standard deviation, knowing that variance is the average of the squared differences from the mean (σ² = Σ(xi - μ)² / N) can provide a deeper understanding of the concept.

6. Knowledge of Data Distribution:

Understanding the concept of a normal distribution and recognizing that data is symmetrically distributed around the mean is important. It's also useful to know about the empirical rule (68-95-99.7 rule) that describes the percentage of data within 1, 2, and 3 standard deviations from the mean in a normal distribution.