Question

Two normal distributions have exactly the same mean, but one has a standard deviation of 20 and the other has a standard deviation of 10. How would the shapes of the two distributions compare?

   Two normal distributions have exactly the same mean, but one has a standard deviation of 20 and the other has a standard deviation of 10. How would the shapes of the two distributions compare?

An Introduction to Psychological Statistics

An Introduction to Psychological Statistics

Garett C. Foster 1st Edition

Chapter 3, Problem 9

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Solved by Expert Hossam Mohamed

02/23/2021

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Both distributions have the same mean, so they are centered at the same point on the horizontal axis. Show more…

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Two normal distributions have exactly the same mean, but one has a standard deviation of 20 and the other has a standard deviation of 10. How would the shapes of the two distributions compare?

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Key Concepts

Standard Deviation

Standard deviation measures the amount of dispersion or spread in a distribution. A larger standard deviation indicates a wider spread of data points around the mean, resulting in a flatter and broader curve, whereas a smaller standard deviation implies that the data points are more tightly clustered around the mean, leading to a steeper and narrower curve.

Normal Distribution

A normal distribution, often depicted as the bell curve, is a symmetric probability distribution that is defined by its mean and standard deviation. It represents how values of a random variable are spread around the mean, with most values clustering around the central peak and tapering off towards the tails.

Mean

The mean is the central value or the 'center of mass' of a distribution. In a normal distribution, the mean determines the center of the curve, meaning that the distribution is symmetric around this point, regardless of how spread out the rest of the data is.

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