Which of these statements about a normally distributed data set is FALSE?


A.)
It is not symmetric around the center.

B.)
Fifty percent of the values are smaller than the mean value.


C.)
Mean, median, and mode are the same value.


D.)
Fifty percent of the values are greater than the mean value.

The false statement about a normally distributed data set is:

**A.) It is not symmetric around the center.**

### Explanation:
- A normally distributed data set **is** symmetric around the center. The mean, median, and mode all coincide at the center of the distribution, which makes the statement that it is not symmetric around the center false.

The other statements are true:
- **B.) Fifty percent of the values are smaller than the mean value.**
- **C.) Mean, median, and mode are the same value.**
- **D.) Fifty percent of the values are greater than the mean value.**

These statements are properties of a normal distribution.

Would you like more details on why these properties hold for a normal distribution? 

Here are some related questions to further your understanding:

1. What is the significance of the standard deviation in a normal distribution?
2. How does the empirical rule apply to a normal distribution?
3. What are z-scores, and how are they used in relation to the normal distribution?
4. Can a data set have more than one mode and still be normally distributed?
5. How does the shape of a distribution change when skewness is introduced?

**Tip:** Remember, in a normal distribution, about 68% of the data falls within one standard deviation of the mean.

Which of these statements about a normally distributed data set is FALSE?

A.) It is not symmetric around the center.

B.) Fifty percent of the values are smaller than the mean value.

C.) Mean, median, and mode are the same value.

D.) Fifty percent of the values are greater than the mean value.

Determine which statement about a normally distributed data set is false. This problem tests understanding of key statistical concepts, including the symmetry of the normal distribution, the relationship between mean, median, and mode, and the distribution of data values. Ideal for students in Grades 9-12.

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