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<!DOCTYPE concept PUBLIC "-//OASIS//DTD DITA Concept//EN" "concept.dtd">
<concept rev="1.2.1" id="appx_median">

  <title>APPX_MEDIAN Function</title>
  <titlealts audience="PDF"><navtitle>APPX_MEDIAN</navtitle></titlealts>
  <prolog>
    <metadata>
      <data name="Category" value="Impala"/>
      <data name="Category" value="SQL"/>
      <data name="Category" value="Developers"/>
      <data name="Category" value="Data Analysts"/>
      <data name="Category" value="Impala Functions"/>
      <data name="Category" value="Aggregate Functions"/>
      <data name="Category" value="Querying"/>
    </metadata>
  </prolog>

  <conbody>

    <p>
      <indexterm audience="hidden">appx_median() function</indexterm>
      An aggregate function that returns a value that is approximately the median (midpoint) of values in the set
      of input values.
    </p>

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

<codeblock>APPX_MEDIAN([DISTINCT | ALL] <varname>expression</varname>)
</codeblock>

    <p>
      This function works with any input type, because the only requirement is that the type supports less-than and
      greater-than comparison operators.
    </p>

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

    <p>
      Because the return value represents the estimated midpoint, it might not reflect the precise midpoint value,
      especially if the cardinality of the input values is very high. If the cardinality is low (up to
      approximately 20,000), the result is more accurate because the sampling considers all or almost all of the
      different values.
    </p>

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

    <p>
      The return value is always the same as one of the input values, not an <q>in-between</q> value produced by
      averaging.
    </p>

<!-- <p conref="../shared/impala_common.xml#common/restrictions_sliding_window"/> -->

    <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/example_blurb"/>

    <p>
      The following example uses a table of a million random floating-point numbers ranging up to approximately
      50,000. The average is approximately 25,000. Because of the random distribution, we would expect the median
      to be close to this same number. Computing the precise median is a more intensive operation than computing
      the average, because it requires keeping track of every distinct value and how many times each occurs. The
      <codeph>APPX_MEDIAN()</codeph> function uses a sampling algorithm to return an approximate result, which in
      this case is close to the expected value. To make sure that the value is not substantially out of range due
      to a skewed distribution, subsequent queries confirm that there are approximately 500,000 values higher than
      the <codeph>APPX_MEDIAN()</codeph> value, and approximately 500,000 values lower than the
      <codeph>APPX_MEDIAN()</codeph> value.
    </p>

<codeblock>[localhost:21000] &gt; select min(x), max(x), avg(x) from million_numbers;
+-------------------+-------------------+-------------------+
| min(x)            | max(x)            | avg(x)            |
+-------------------+-------------------+-------------------+
| 4.725693727250069 | 49994.56852674231 | 24945.38563793553 |
+-------------------+-------------------+-------------------+
[localhost:21000] &gt; select appx_median(x) from million_numbers;
+----------------+
| appx_median(x) |
+----------------+
| 24721.6        |
+----------------+
[localhost:21000] &gt; select count(x) as higher from million_numbers where x &gt; (select appx_median(x) from million_numbers);
+--------+
| higher |
+--------+
| 502013 |
+--------+
[localhost:21000] &gt; select count(x) as lower from million_numbers where x &lt; (select appx_median(x) from million_numbers);
+--------+
| lower  |
+--------+
| 497987 |
+--------+
</codeblock>

    <p>
      The following example computes the approximate median using a subset of the values from the table, and then
      confirms that the result is a reasonable estimate for the midpoint.
    </p>

<codeblock>[localhost:21000] &gt; select appx_median(x) from million_numbers where x between 1000 and 5000;
+-------------------+
| appx_median(x)    |
+-------------------+
| 3013.107787358159 |
+-------------------+
[localhost:21000] &gt; select count(x) as higher from million_numbers where x between 1000 and 5000 and x &gt; 3013.107787358159;
+--------+
| higher |
+--------+
| 37692  |
+--------+
[localhost:21000] &gt; select count(x) as lower from million_numbers where x between 1000 and 5000 and x &lt; 3013.107787358159;
+-------+
| lower |
+-------+
| 37089 |
+-------+
</codeblock>
  </conbody>
</concept>