Standard Deviation
Standard Deviation - Related Videos
01:10
Standard Deviation
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2023
The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more...
01:27
Standard Deviation
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2024
Standard Deviation Standard deviation is a statistical measure quantifying the degree of variation or dispersion in a set of values. It is particularly useful in finance for assessing the volatility and risk associated with investment returns. By calculating the standard deviation, investors can gain a clearer understanding of how much an investment's returns deviate from the mean return over a given period, thus providing insight into the investment's overall risk profile. To compute the...
02:32
Variation: Normal Distribution, Range, and Standard Deviation
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2020
In the field of psychology, there are several ways to organize measurements of a trait, feature, or characteristic (i.e., variables). Qualitative data, such as ethnicity, can be tabulated into a frequency count to provide information about the proportion, as well as the variety of groups in a sample or population. On the other hand, researchers can perform a wider set of calculations on quantitative data. The mean, mode, and median, for instance, are central tendency measures to identify a...
01:14
Standard Deviation of Calculated Results
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2024
Standard deviation measures the spread of data around the mean value. Many large data sets follow a Gaussian distribution, also known as a normal distribution. This distribution is bell-shaped curved, with the most frequently observed value (mean or central value) in the middle. The farther away from the central value, the greater the deviation from the central value, and the lower the frequency. A broad Gaussian distribution curve has a wider standard deviation, representing a data set with...
01:08
Calculating Standard Deviation
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2023
The standard deviation is the most common measure of variation. It is a value that tells us how far a data value is from the mean value in a dataset. Further, the standard deviation is always a positive value or zero. The standard deviation value is small when all the data is concentrated close to the mean. Here the data exhibits low variation. The standard deviation value is larger when the data values are more spread out from the mean. Here, the data displays high variation. Let us...
FAQs
Squaring each deviation prevents positive and negative differences from canceling one another before the values are averaged. It also makes larger departures from the mean contribute more strongly than smaller departures. Consequently, the final square-rooted result responds to how far observations are distributed around the mean, helping distinguish tightly clustered psychological measurements from highly variable ones.
A larger value signals that observations are less consistent around their mean, whereas a smaller value indicates greater concentration near that mean. The measure does not indicate whether scores are generally high or low; that interpretation comes from the mean. Used together, the two statistics show both the central level and the amount of variation in a psychological dataset.
Because the calculation uses each observation’s distance from the mean and squares it, a value far from the mean contributes substantially to the resulting average. This makes standard deviation sensitive to unusually high or low psychological observations. Reviewing those observations alongside the measure can help researchers recognize whether the dataset contains especially atypical scores or reaction times.
Comparing group means shows whether their average outcomes differ, while comparing standard deviations shows whether their observations vary to similar or different degrees. Two groups can have comparable means but markedly different consistency. For psychological studies, considering both statistics provides a fuller comparison of test scores, symptom ratings, reaction times, or other measured behaviors.
The measure can summarize variability in test scores, reaction times, symptom ratings, and other behavioral observations. Its value is not limited to one type of psychological instrument; it applies whenever researchers examine individual values around a dataset’s mean. This allows investigators to describe whether participants’ measurements are relatively consistent or widely dispersed within the study data.
Standard deviation supplies information about the spread of observations that the mean alone cannot provide. In psychological research, that information supports interpretation of datasets and comparisons between groups, while also helping identify unusually high or low observations. It therefore contributes context when researchers analyze behavioral measurements rather than treating average scores as a complete summary.