What is standard deviation?
The standard deviation is the most frequently calculated measure of variability. The standard deviation value represents the average distance of a set of scores from the mean. Standard deviation and the normal curve Knowing the standard deviation helps create a more accurate picture of the distribution along the normal curve. A smaller standard deviation represents a data set where scores are very close in value to the mean; a smaller range. A data set with a larger standard deviation has scores with more variance; a larger range. For example, if the average score on a test was 80 and the standard deviation was 2, the scores would be more clustered around the mean than if the standard deviation was 10. Figure 1. The normal curve. Standard deviation is a constant interval from the mean. Roll the mouse over the curve to discover the percentage each portion represents. Calculating the standard deviation The figure below displays the formula for calculating the standard deviation. (It is m
Standard deviation is a statistical value used to determine how spread out the data in a sample are, and how close individual data points are to the mean, or average, value of the sample. A standard deviation of a data set equal to zero indicates that all values in the set are the same. A larger value implies that the individual data points are farther from the average value. In a normal distribution of data, also known as a bell curve, the majority of the data in the distribution — approximately 68% — will fall within plus or minus one standard deviation of the statistical average. This means that if the standard deviation of a data set is 2, for example, the majority of data in the set will fall within 2 more or 2 less than the average. Roughly 95.5% of normally distributed data is within two standard deviations of the mean, and over 99% are within three. To calculate the standard deviation, statisticians first calculate the mean value of all the data points. The mean, or average, is
The most insightful and dependable barometer for all funds, standard deviation reflects the degree to which returns fluctuate around their average. It is usually based on monthly returns over the past 36 months. The higher the number, the greater the volatility; for a stock fund that has an average annual return of 12% and a standard deviation of 20%, you can expect to earn between 32% and -8% in about two out of every three years.
