What does variance show

Active 5 months ago. Viewed k times. Furthermore, why do you really need a standard deviation? Improve this question. Le Max Le Max 3, 9 9 gold badges 25 25 silver badges 26 26 bronze badges.

Still this link has the simplest and best explanation. If measuring meters, the standard deviation will be meters. Variance, in contrast, will be meters squared. Add a comment. Active Oldest Votes. Improve this answer. Peter Flom Peter Flom Why do I really ned two parameters to show the same thing the deviation around the arithmetical mean For developing the theory the variance is better. Say, a sample of adult heights is in meters, then standard deviation will also be in meters.

A similar expression exists in the general case without independence with a correction using covariance terms. In general, the square root transformation complicates things and makes standard deviation more difficult to work with analytically. Show 3 more comments. John John 21k 9 9 gold badges 47 47 silver badges 83 83 bronze badges.

However, to answer your question, there are several points that can be added: The mean and variance are the two parameters that determine a normal distribution. The margin of error is expressed as a multiple of the standard deviation of the estimate.

Michael R. Chernick Michael R. Chernick Then you take each value in data set, subtract the mean and square the difference. For instance, for the first value:. The variance is To get the standard deviation, you calculate the square root of the variance, which is 3.

Standard deviation is useful when comparing the spread of two separate data sets that have approximately the same mean. The data set with the smaller standard deviation has a narrower spread of measurements around the mean and therefore usually has comparatively fewer high or low values. An item selected at random from a data set whose standard deviation is low has a better chance of being close to the mean than an item from a data set whose standard deviation is higher.

However, standard deviation is affected by extreme values. A single extreme value can have a big impact on the standard deviation.

For example, original data containing lengths measured in feet has a standard deviation also measured in feet. A normal curve is a symmetric, bell-shaped curve. The center of the graph is the mean, and the height and width of the graph are determined by the standard deviation. When the standard deviation is small, the curve will be tall and narrow in spread.

When the standard deviation is large, the curve will be short and wide in spread. The mean and median have the same value in a normal curve. Normal Curve Empirical Rule: Approximately IQR for a normal curve is 1.

Variance measures how far a set of data is spread out. A variance of zero indicates that all of the data values are identical. All non-zero variances are positive. The process of finding the variance is very similar to finding the MAD, mean absolute deviation. The only difference is the squaring of the distances. Process: 1 Find the mean average of the set.