Sample Variance
Sample Variance - Related Videos
01:25
Variance
0 Views •
2024
Variance is a statistical measure that quantifies the degree of risk associated with an investment's returns by indicating how much the returns deviate from their expected value over time. It provides essential insights into the stability and predictability of an investment's performance. The variance calculation involves determining the mean return, which is the average return over a specified period, and then calculating the deviations of each return from this mean. These deviations are...
01:15
Variance
0 Views •
2023
The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.The standard deviation measures the spread in the same units as the data.
01:21
Friedman Two-way Analysis of Variance by Ranks
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2025
Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures from...
08:18
Design and Use of a Full Flow Sampling System (FFS) for the Quantification of Methane Emissions
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Cited by 13 •
2016
We have designed, developed, and implemented a novel full flow sampling system (FFS) for quantification of methane emissions and greenhouse gases from across the natural gas supply chain.
06:33
Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding
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Cited by 10 •
2018
Here we present a protocol for decomposing the variance in reading comprehension into the unique and common effects of language and decoding.
FAQs
Bessel’s correction makes sample variance appropriate for estimating population variability from a random sample. Dividing by n would systematically use the sample size as the denominator, whereas dividing by n−1 adjusts the estimate so that, across random samples, it is unbiased for the population variance. The correction matters when the goal is inference beyond the observed data, not merely description of that sample.
Squaring the deviations prevents differences above and below the sample mean from canceling each other. It also gives larger departures a stronger contribution to the total. The resulting measure therefore summarizes dispersion using squared measurement units, which distinguishes variance from measures expressed in the original units of the observations.
Sample standard deviation is obtained by taking the square root of sample variance. This transformation preserves the underlying assessment of dispersion while returning the result to the original measurement units. Variance is useful in statistical calculations involving variability, whereas standard deviation is often easier to interpret when describing how widely observations differ from their sample mean.
A sample variance estimates population variance most appropriately when the observations form a random sample from that population. Random sampling is the condition linked to the unbiasedness provided by n−1. If the sample is not random, the correction alone does not guarantee that the calculated value represents population variability, so conclusions about the larger population require caution.
Sample variance supports uncertainty assessment, hypothesis testing, and confidence intervals because these activities require information about how observations vary within a sample. It can contribute to inference about a larger population while also describing variability in the observed data. Its role depends on whether the analysis emphasizes estimation, testing, interval construction, or comparison of dispersion.
Calculate sample variance separately for each group using the same n−1 correction, then compare the resulting values. A larger variance indicates greater dispersion around that group’s sample mean, while a smaller value indicates less dispersion. Because variance uses squared units, sample standard deviation may be easier to communicate when groups share the same measurement scale.