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100 lines
2.4 KiB
Markdown
100 lines
2.4 KiB
Markdown
---
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title: "varPop"
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slug: "/en/sql-reference/aggregate-functions/reference/varpop"
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sidebar_position: 32
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---
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This page covers the `varPop` and `varPopStable` functions available in ClickHouse.
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## varPop
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Calculates the population covariance between two data columns. The population covariance measures the degree to which two variables vary together. Calculates the amount `Σ((x - x̅)^2) / n`, where `n` is the sample size and `x̅`is the average value of `x`.
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**Syntax**
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```sql
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covarPop(x, y)
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```
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**Parameters**
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- `x`: The first data column. [Numeric](../../../native-protocol/columns.md)
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- `y`: The second data column. [Numeric](../../../native-protocol/columns.md)
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**Returned value**
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Returns an integer of type `Float64`.
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**Implementation details**
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This function uses a numerically unstable algorithm. If you need numerical stability in calculations, use the slower but more stable [`varPopStable` function](#varPopStable).
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**Example**
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```sql
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DROP TABLE IF EXISTS test_data;
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CREATE TABLE test_data
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(
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x Int32,
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y Int32
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)
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ENGINE = Memory;
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INSERT INTO test_data VALUES (1, 2), (2, 3), (3, 5), (4, 6), (5, 8);
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SELECT
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covarPop(x, y) AS covar_pop
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FROM test_data;
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```
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```response
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3
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```
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## varPopStable
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Calculates population covariance between two data columns using a stable, numerically accurate method to calculate the variance. This function is designed to provide reliable results even with large datasets or values that might cause numerical instability in other implementations.
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**Syntax**
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```sql
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covarPopStable(x, y)
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```
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**Parameters**
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- `x`: The first data column. [String literal](../syntax#syntax-string-literal)
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- `y`: The second data column. [Expression](../syntax#syntax-expressions)
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**Returned value**
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Returns an integer of type `Float64`.
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**Implementation details**
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Unlike [`varPop()`](#varPop), this function uses a stable, numerically accurate algorithm to calculate the population variance to avoid issues like catastrophic cancellation or loss of precision. This function also handles `NaN` and `Inf` values correctly, excluding them from calculations.
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**Example**
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Query:
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```sql
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DROP TABLE IF EXISTS test_data;
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CREATE TABLE test_data
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(
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x Int32,
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y Int32
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)
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ENGINE = Memory;
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INSERT INTO test_data VALUES (1, 2), (2, 9), (9, 5), (4, 6), (5, 8);
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SELECT
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covarPopStable(x, y) AS covar_pop_stable
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FROM test_data;
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```
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```response
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0.5999999999999999
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```
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