To determine which data sets do not represent a normal distribution, we need to understand the characteristics of a normal distribution first. A normal distribution, also known as a Gaussian distribution, generally has the following properties:
1. Approximately 68% of the data lies within one standard deviation of the mean.
2. The mean is equal to the median.
3. The data is symmetric around the mean.
Now, let's evaluate each provided data set description to see which ones do not conform to these properties:
1. A data set where 50% of the data are more than 1 standard deviation from the mean
- A normal distribution would have around 68% of the data within 1 standard deviation from the mean. If 50% of the data are more than 1 standard deviation away from the mean, this doesn't align with the characteristic properties of a normal distribution. Therefore, this description is not a normal distribution.
2. A data set where the mean is 12 and the median is 12
- In a normal distribution, the mean is equal to the median. Given that the mean and the median are both 12, this data set could represent a normal distribution.
3. A data set that has a mean of 15 and a median of 9
- For a normal distribution, the mean and median should be approximately equal. In this case, the mean and median are significantly different, which indicates the data set is likely not a normal distribution.
4. A data set that is asymmetrical
- A normal distribution is symmetric. So, an asymmetrical data set does not fit the characteristics of a normal distribution.
5. A data set where most values are close to the mean
- In a normal distribution, most values should be close to the mean, within one standard deviation. This description fits the attributes of a normal distribution.
Given this analysis, the descriptions that do not represent a normal distribution are:
- A data set where 50% of the data are more than 1 standard deviation from the mean
- A data set that has a mean of 15 and a median of 9
- A data set that is asymmetrical
Therefore, the correct answers are:
- A data set where 50% of the data are more than 1 standard deviation from the mean
- A data set that has a mean of 15 and a median of 9
- A data set that is asymmetrical
