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Your question is a bit difficult to answer, as "succinct" is usually a quality in reference to a description or explanation. It is defined by Webster's dictionary as "marked by compact precise expression without wasted words." See related link.
For this reason, I have reworded your question as follows: Does the variance fully describe or summarize the raw data? The answer is no.
For any set of data, many statistical measures can be calculated, including the mean and variance. The variance or more commonly the square of the variance (standard deviation) is a very useful in identifying the dispersion of data, but is incomplete in fully describing the data. The mean is also important. Graphs can improve the summarization of data in a more visual manner.
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What is the purpose of calculating the mean and the variance?
Calculating the mean helps to understand the central tendency of a data set, while calculating the variance provides information about the spread or dispersion of the data points around the mean. Together, the mean and variance provide a summary of the data distribution, enabling comparisons and making statistical inferences.
Does variance and standard deviation assume nominal data?
No. Variance and standard deviation are dependent on, but calculated irrespective of the data. You do, of course, have to have some variation, otherwise, the variance and standard deviation will be zero.
What is the variance of this data set 10 8 8 6 5?
The variance is: 3.8
The mean is 10 What is the variance of the data set 4 9 9 13?
The variance is 13.5833
What is the variance with sample data set 9 14 19 16 8 6 17 11 18?
The variance of this data set is 22.611
What is the significance of variance in statistics?
Variance is a measure of "relative to the mean, how far away does the other data fall" - it is a measure of dispersion. A high variance would indicate that your data is very much spread out over a large area (random), whereas a low variance would indicate that all your data is very similar.Standard deviation (the square root of the variance) is a measure of "on average, how far away does the data fall from the mean". It can be interpreted in a similar way to the variance, but since it is square rooted, it is less susceptible to outliers.
How many cases are needed for analysis of variance?
There only needs to be one data point to calculate variance.
Is variance square of standard deviation?
Yes, the variance of a data set is the square of the standard deviation (sigma) of the set. This means that the variance is always a positive number, even though the data might have a negative sigma value.
If the variance of the data a population is 256 what is the standard deviation of the data values?
16
Can the variance for a set of data be a negative value?
yes
Is mean used to describe the variance of data?
Yes.
What is the variance If the standard deviation of some data is 36?
Variance = (std dev) ^2 = 36^2 = 1296.
