Manuals/calci/VARPIF

VARPIF (Array,Condition,SumArray)

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Array} is the set of values.
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Condition} is the particular condition value.

Description

• This function gives the variance based on the entire population which satisfies the given condition.
• In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle VARPIF (Array,Condition,SumArray)} ,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Array} is the set of values.
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Condition} is the particular condition which satisfies the variance values.
• Variance is a measure of dispersion obtained by taking the mean of the squared deviations of the observed values from their mean in a frequency distribution.
• i.e.,variance is a measure of how far each value in the data set is from the mean.
• It is denoted by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma } .
• The square root of variance is called the standard deviation.
• To find the variance we can use the following formula:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Variance= \frac{\sum (x_i-\bar{x})^2}{n-1}} where ${\bar {x}}$ is the sample mean of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_i} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n } is the sample size.

• Suppose Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma = 0} which is indicating all the values are identical.
• When Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma } is non-zero then it is always positive.
• This function is considering our given data is the entire population.
• Suppose it should consider the data as the sample of the population, we can use the VAR function.
• The arguments can be either numbers or names, array,constants or references that contain numbers.
• Suppose the array contains text,logical values or empty cells, like that values are not considered.
• When we are entering logical values and text representations of numbers as directly, then the arguments are counted.
• Suppose the function have to consider the logical values and text representations of numbers in a reference , we can use the VARPA function.
• This function will return the result as error when

      1. Any one of the argument is non-numeric. 
      2. The arguments containing the error values or text that cannot be translated in to numbers.

Examples

1. VARPIF([12,32,45,10,56],">10") = 268.1875
2. VARPIF([14.2,67.3,19.34,20.6,16.02,78.4,54.9],">21") = 92.1355555555556
3. VARPIF([14.2,67.3,19.34,20.6,16.02,78.4,54.9],"<21") = 6.517400000000003

See Also

• VAR
• VARP
• VARA

References

• Variance

• List of Main Z Functions
• Z3 home