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Statistical Excel 2010 ◉ 9 views

=COVARIANCE.P()

Returns population covariance, the average of the products of deviations for each data point pair in two data sets. Use covariance to determine the relationship between two data sets.

Applies To: Excel for Microsoft 365Excel for Microsoft 365 for MacExcel 2024Excel 2024 for MacExcel 2021Excel 2021 for MacExcel 2019Excel 2016
=COVARIANCE.P(array1,array2)
Hover argument names in the table for details.
Output typeNumber
Popularity12 / 100
VolatileNo
Dynamic ArrayNo
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◧ Arguments

ArgumentTypeRequiredDescription
array1 Array Required The first cell range of integers.
array2 Array Required The second cell range of integers.

▣ Examples

▦ Data
CellValue
A2 Data1
B2 Data2
A3 3
B3 9
A4 2
B4 7
A5 4
B5 12
A6 5
B6 15
A7 6
B7 17
A8 Data1
B8 Data2
A9 3
B9 9
A10 2
B10 7
A11 4
B11 12
A12 5
B12 15
A13 6
B13 17
Covariance, the average of the products of deviations for each data point pair above =COVARIANCE.P(A2:A6, B2:B6)
Result: 5.2

§ Remarks

  • The arguments must either be numbers or be names, arrays, or references that contain numbers.
  • If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.
  • If array1 and array2 have different numbers of data points, COVARIANCE.P returns the #N/A error value.
  • If either array1 or array2 is empty, COVARIANCE.P returns the #DIV/0! error value.
  • The covariance is: where are the sample means AVERAGE(array1) and AVERAGE(array2), and n is the sample size.

✦ Tips

  • The arguments must either be numbers or be names, arrays, or references that contain numbers.
  • If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.
  • The covariance is: where are the sample means AVERAGE(array1) and AVERAGE(array2), and n is the sample size.

⚠ Common Errors

#N/A If array1 and array2 have different numbers of data points, COVARIANCE.P returns the #N/A error value.
Fix: Make the two ranges the same size
#DIV/0! If either array1 or array2 is empty, COVARIANCE.P returns the #DIV/0! error value.
Fix: مطمئن شوید هر دو محدوده حداقل یک مقدار عددی دارند.

⇄ Related Functions

=COVARIANCE.S() Returns the sample covariance, the average of the products of deviations for each data point pair in two data sets. =VAR.P() Calculates variance based on the entire population (ignores logical values and text in the population). =CORREL() The CORREL function returns the correlation coefficient of two cell ranges. Use the correlation coefficient to determine the relationship between two properties. For example, you can examine the relationship between a location's average temperature and the use of air conditioners.

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