How is finding the standard deviation a measurement of a data\'s center?
my teacher said it measured the center...
Perhaps this explanation will help you.
http://en.wikipedia.org/wiki/Standard_deviation
The standard deviation is not a measurement of a data's center, but rather a measurement of the spread or dispersion of the data. It tells us how far the data values are spread out from the mean (average) of the data set.
To find the standard deviation, you need to follow these steps:
1. Calculate the mean (average) of the data set.
2. Subtract the mean from each data point, and square the result.
3. Find the mean of the squared differences.
4. Take the square root of the mean of the squared differences.
The result is the standard deviation. It indicates the typical or average amount by which each data point deviates from the mean.
The measurement of a data's center is typically represented by the mean, median, or mode. The mean is found by summing all the data values and dividing by the total count of values. The median is the middle value of a sorted data set, and the mode is the most frequently occurring value. These measures provide insights into the central tendency of the data, whereas the standard deviation describes the variability or dispersion from the center.