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<!DOCTYPE concept PUBLIC "-//OASIS//DTD DITA Concept//EN" "concept.dtd">
<concept rev="1.4" id="variance">

  <title>VARIANCE, VARIANCE_SAMP, VARIANCE_POP, VAR_SAMP, VAR_POP Functions</title>
  <titlealts audience="PDF"><navtitle>VARIANCE, VARIANCE_SAMP, VARIANCE_POP, VAR_SAMP, VAR_POP</navtitle></titlealts>
  <prolog>
    <metadata>
      <data name="Category" value="Impala"/>
      <data name="Category" value="SQL"/>
      <data name="Category" value="Impala Functions"/>
      <data name="Category" value="Aggregate Functions"/>
      <data name="Category" value="Querying"/>
      <data name="Category" value="Developers"/>
      <data name="Category" value="Data Analysts"/>
    </metadata>
  </prolog>

  <conbody>

    <p>
      <indexterm audience="hidden">variance() function</indexterm>
      <indexterm audience="hidden">variance_samp() function</indexterm>
      <indexterm audience="hidden">variance_pop() function</indexterm>
      <indexterm audience="hidden">var_samp() function</indexterm>
      <indexterm audience="hidden">var_pop() function</indexterm>
      An aggregate function that returns the
      <xref href="http://en.wikipedia.org/wiki/Variance" scope="external" format="html">variance</xref> of a set of
      numbers. This is a mathematical property that signifies how far the values spread apart from the mean. The
      return value can be zero (if the input is a single value, or a set of identical values), or a positive number
      otherwise.
    </p>

    <p conref="../shared/impala_common.xml#common/syntax_blurb"/>

<codeblock>{ VARIANCE | VAR[IANCE]_SAMP | VAR[IANCE]_POP } ([DISTINCT | ALL] <varname>expression</varname>)</codeblock>

    <p>
      This function works with any numeric data type.
    </p>

    <p conref="../shared/impala_common.xml#common/former_odd_return_type_string"/>

    <p>
      This function is typically used in mathematical formulas related to probability distributions.
    </p>

    <p>
      The <codeph>VARIANCE_SAMP()</codeph> and <codeph>VARIANCE_POP()</codeph> functions compute the sample
      variance and population variance, respectively, of the input values. (<codeph>VARIANCE()</codeph> is an alias
      for <codeph>VARIANCE_SAMP()</codeph>.) Both functions evaluate all input rows matched by the query. The
      difference is that <codeph>STDDEV_SAMP()</codeph> is scaled by <codeph>1/(N-1)</codeph> while
      <codeph>STDDEV_POP()</codeph> is scaled by <codeph>1/N</codeph>.
    </p>

    <p rev="2.0.0">
      The functions <codeph>VAR_SAMP()</codeph> and <codeph>VAR_POP()</codeph> are the same as
      <codeph>VARIANCE_SAMP()</codeph> and <codeph>VARIANCE_POP()</codeph>, respectively. These aliases are
      available in Impala 2.0 and later.
    </p>

    <p>
      If no input rows match the query, the result of any of these functions is <codeph>NULL</codeph>. If a single
      input row matches the query, the result of any of these functions is <codeph>"0.0"</codeph>.
    </p>

    <p conref="../shared/impala_common.xml#common/example_blurb"/>

    <p>
      This example demonstrates how <codeph>VARIANCE()</codeph> and <codeph>VARIANCE_SAMP()</codeph> return the
      same result, while <codeph>VARIANCE_POP()</codeph> uses a slightly different calculation to reflect that the
      input data is considered part of a larger <q>population</q>.
    </p>

<codeblock>[localhost:21000] &gt; select variance(score) from test_scores;
+-----------------+
| variance(score) |
+-----------------+
| 812.25          |
+-----------------+
[localhost:21000] &gt; select variance_samp(score) from test_scores;
+----------------------+
| variance_samp(score) |
+----------------------+
| 812.25               |
+----------------------+
[localhost:21000] &gt; select variance_pop(score) from test_scores;
+---------------------+
| variance_pop(score) |
+---------------------+
| 811.438             |
+---------------------+
</codeblock>

    <p>
      This example demonstrates that, because the return value of these aggregate functions is a
      <codeph>STRING</codeph>, you convert the result with <codeph>CAST</codeph> if you need to do further
      calculations as a numeric value.
    </p>

<codeblock>[localhost:21000] &gt; create table score_stats as select cast(stddev(score) as decimal(7,4)) `standard_deviation`, cast(variance(score) as decimal(7,4)) `variance` from test_scores;
+-------------------+
| summary           |
+-------------------+
| Inserted 1 row(s) |
+-------------------+
[localhost:21000] &gt; desc score_stats;
+--------------------+--------------+---------+
| name               | type         | comment |
+--------------------+--------------+---------+
| standard_deviation | decimal(7,4) |         |
| variance           | decimal(7,4) |         |
+--------------------+--------------+---------+
</codeblock>

    <p conref="../shared/impala_common.xml#common/restrictions_blurb"/>

    <p conref="../shared/impala_common.xml#common/analytic_not_allowed_caveat"/>

    <p conref="../shared/impala_common.xml#common/related_info"/>

    <p>
      The <codeph>STDDEV()</codeph>, <codeph>STDDEV_POP()</codeph>, and <codeph>STDDEV_SAMP()</codeph> functions
      compute the standard deviation (square root of the variance) based on the results of
      <codeph>VARIANCE()</codeph>, <codeph>VARIANCE_POP()</codeph>, and <codeph>VARIANCE_SAMP()</codeph>
      respectively. See <xref href="impala_stddev.xml#stddev"/> for details about the standard deviation property.
    </p>
  </conbody>
</concept>