Question

If the standard deviation of a data set is 4, what is the variance? 

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Answer 1

Standard deviation( σ)$= 4$

The Formula is Variance = σ2

Variance =$(4)2$⇒ Variance $= 16$

∴ The value of variance is $16$.

A standard deviation is a measure of how the data is broken down in relation to the definition.

The standard deviation close to zero indicates that the data points are closer to the definition, while the higher or lower standard deviations indicate the data points in the sequence above or below the definition.

Answer 2

Answer:

Concept:

The standard deviation is a statistics that describes the degree of volatility or dispersion in a set of numerical values. A low standard deviation indicates that values tend to be close to the mean (also known as the predicted value) of the collection, whereas a large standard deviation denotes that values are distributed over a wider range. Standard deviation is most usually denoted in mathematical texts and equations by the lower case Greek letter (sigma), which stands for the population standard deviation, or by the Latin symbol s, which stands for the sample standard deviation.

Given:

What is the variance of a set of data if the standard deviation is 4?

Find:

find the variance for the given question

Answer:

standard deviation = 4

variance = σ²

$variance=4^{2}$

$variance=16$

• The term "standard deviation" (or σ) refers to a measurement of the data's dispersion from the mean. While a high standard deviation indicates that the data are more spread, a low standard deviation suggests that the data are clustered around the mean.
• In probability and statistics, variance is the estimated value of the squared variation of a random variable out of its mean value. Informally,
• variance calculates the degree to which a random group of numbers deviates from the mean value.
• Data points' variance from the mean is a measure of how they vary. A variance, according to Layman, is a measurement of how widely apart a set of data (numbers) are from their mean (average) value.
• Finding the expected amount of deviation from the actual number is what is meant by variance. As a result, variance is influenced by the data set's standard deviation.
• Data is more dispersed from its mean the higher the variance value, and less dispersed from mean if the variance value is low or minimal. As a result, it is referred to as a measure of data spread from mean.

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