Questions: What do we mean when we say that a distribution is symmetric? Give simple examples of a symmetric distribution, a left-skewed distribution, and a right-skewed distribution. What do we mean when we say that a distribution is symmetric? A. A single-peaked distribution is symmetric if its values are more spread out on the right side of the mode. B. A single-peaked distribution is symmetric if its values are more spread out on the left side of the mode. C. A single-peaked distribution is symmetric if its left half has as many data values as the right half. D. A single-peaked distribution is symmetric if its left half is a mirror image of its right half. Give a simple example of a symmetric distribution. Choose the correct answer below. A. The speed of cars on a road where a visible patrol car is using radar to detect speeders is a symmetric distribution. B. The heights of a sample of 100 women is a symmetric distribution. C. The number of books read quring the school year by fifth graders is a symmetric distribution. D. The weights of a sample of 500 dogs of varying breed is a symmetric distribution.

What do we mean when we say that a distribution is symmetric? Give simple examples of a symmetric distribution, a left-skewed distribution, and a right-skewed distribution. What do we mean when we say that a distribution is symmetric? A. A single-peaked distribution is symmetric if its values are more spread out on the right side of the mode. B. A single-peaked distribution is symmetric if its values are more spread out on the left side of the mode. C. A single-peaked distribution is symmetric if its left half has as many data values as the right half. D. A single-peaked distribution is symmetric if its left half is a mirror image of its right half. Give a simple example of a symmetric distribution. Choose the correct answer below. A. The speed of cars on a road where a visible patrol car is using radar to detect speeders is a symmetric distribution. B. The heights of a sample of 100 women is a symmetric distribution. C. The number of books read quring the school year by fifth graders is a symmetric distribution. D. The weights of a sample of 500 dogs of varying breed is a symmetric distribution.
Transcript text: What do we mean when we say that a distribution is symmetric? Give simple examples of a symmetric distribution, a left-skewed distribution, and a right-skewed distribution. What do we mean when we say that a distribution is symmetric? A. A single-peaked distribution is symmetric if its values are more spread out on the right side of the mode. B. A single-peaked distribution is symmetric if its values are more spread out on the left side of the mode. C. A single-peaked distribution is symmetric if its left half has as many data values as the right half. D. A single-peaked distribution is symmetric if its left half is a mirror image of its right half. Give a simple example of a symmetric distribution. Choose the correct answer below. A. The speed of cars on a road where a visible patrol car is using radar to detect speeders is a symmetric distribution. B. The heights of a sample of 100 women is a symmetric distribution. C. The number of books read quring the school year by fifth graders is a symmetric distribution. D. The weights of a sample of 500 dogs of varying breed is a symmetric distribution.
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Solution

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Solution Steps

Step 1: Understanding Symmetric Distribution

A distribution is symmetric if its left half is a mirror image of its right half. This means that the data is evenly distributed around the center, and the shape of the distribution is the same on both sides of the center.

Step 2: Identifying the Correct Definition of Symmetric Distribution

From the given options:

  • Option A is incorrect because it describes a right-skewed distribution.
  • Option B is incorrect because it describes a left-skewed distribution.
  • Option C is incorrect because it only mentions the number of data values, not the mirror image property.
  • Option D is correct because it states that the left half is a mirror image of the right half, which is the definition of a symmetric distribution.
Step 3: Providing an Example of a Symmetric Distribution

From the given options:

  • Option A is incorrect because the speed of cars on a road with a visible patrol car is likely to be skewed, not symmetric.
  • Option B is correct because the heights of a sample of 100 women are likely to follow a symmetric distribution, such as a normal distribution.
  • Option C is incorrect because the number of books read by fifth graders is likely to be skewed, not symmetric.
  • Option D is incorrect because the weights of dogs of varying breeds are likely to be skewed, not symmetric.

Final Answer

  1. The correct answer is D.
  2. The correct answer is B.
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