Final Answer:
The statement that is false is that the standard deviation (denoted as s) is always a positive number.
Explanation:
The standard deviation (denoted as s) is a measure of the spread of data around the mean. It is calculated as the square root of the variance. The variance is defined as the average of the squared differences from the mean. When the mean is zero, the variance is the same as the average of the squared values. This means the standard deviation can be both positive and negative.
When the data is normally distributed, the standard deviation is always a positive number. This is because the normal distribution is symmetric around the mean with most of the data points lying within one standard deviation of the mean. This means that the standard deviation will always be positive in a normal distribution.
However, when the data is not normally distributed, the standard deviation can be either positive or negative. This is because the data is not as concentrated around the mean as it is in a normal distribution. The standard deviation can be negative if the data is skewed in one direction and the mean is not at the centre of the data points.
In summary, the statement that is false is that the standard deviation (denoted as s) is always a positive number. The standard deviation can be either positive or negative depending on the distribution of the data.