Questions: Which of the following is always true? Choose the correct answer below. A. In a symmetric and bell-shaped distribution, the mean, median, and mode are the same. B. The mean and median should be used to identify the shape of the distribution. C. Data skewed to the right have a longer left tail than right tail. D. For skewed data, the mode is farther out in the longer tail than the median.

Which of the following is always true?

Choose the correct answer below.
A. In a symmetric and bell-shaped distribution, the mean, median, and mode are the same.
B. The mean and median should be used to identify the shape of the distribution.
C. Data skewed to the right have a longer left tail than right tail.
D. For skewed data, the mode is farther out in the longer tail than the median.

Transcript text: Which of the following is always true? Choose the correct answer below. A. In a symmetric and bell-shaped distribution, the mean, median, and mode are the same. B. The mean and median should be used to identify the shape of the distribution. C. Data skewed to the right have a longer left tail than right tail. D. For skewed data, the mode is farther out in the longer tail than the median.

Solution

Solution Steps

Step 1: Analyze Option A

Option A states: "In a symmetric and bell-shaped distribution, the mean, median, and mode are the same."
This is a fundamental property of symmetric distributions, particularly the normal distribution. In such cases, the mean, median, and mode coincide at the center of the distribution.
Conclusion: This statement is true.

Step 2: Analyze Option B

Option B states: "The mean and median should be used to identify the shape of the distribution."
While the mean and median can provide some insight into the shape of the distribution (e.g., skewness), they are not sufficient on their own to fully identify the shape. Other measures, such as skewness and kurtosis, are also needed.
Conclusion: This statement is not always true.

Step 3: Analyze Option C

Option C states: "Data skewed to the right have a longer left tail than right tail."
This is incorrect. Data skewed to the right have a longer right tail, not a longer left tail.
Conclusion: This statement is false.