[doc](agg) add doc for sem

docs/sql-manual/sql-functions/aggregate-functions/sem.md

@@ -0,0 +1,95 @@
+---
+{
+"title": "SEM",
+"language": "en"
+}
+---
+
+## Description
+
+Calculate the standard error of the mean for all non-null values in the specified column or expression.
+
+## Syntax
+
+```text
+SEM([DISTINCT] <expr>)
+```
+
+## Parameters
+
+| Parameter | Description |
+| -- | -- |
+| `<expr>` | An expression or column, typically a numeric column or an expression that can be converted to a numeric value, supporting the Double data type.|
+| `[DISTINCT]` | An optional keyword indicating that the mean standard error should be calculated after removing duplicate values in expr.。 |
+
+## Return Value
+
+Returns a Double. Returns the standard error of the mean for the selected column or expression. If all records within the group are NULL, the function returns NULL.
+
+## Examples
+
+```sql
+-- setup
+create table t1(
+        id int,
+        k_double double,
+) distributed by hash (id) buckets 1
+properties ("replication_num"="1");
+insert into t1 values 
+    (1, 222.222),
+    (2, 3.3),
+    (3, 3.3),
+    (4, null);
+```
+
+```sql
+select sem(k_double) from t1;
+```
+
+Calculation of the mean for the Double type: the mean and standard error for [222.222, 3.3, 3.3, null] is 72.974.
+
+```text
++---------------+
+| sem(k_double) |
++---------------+
+|        72.974 |
++---------------+
+```
+
+```sql
+select sem(cast(null as double)) from t1;
+```
+
+When all values are null, return null.
+
+```text
++---------------------------+
+| sem(cast(null as double)) |
++---------------------------+
+|                      NULL |
++---------------------------+
+```
+
+```sql
+select sem(distinct k_double) from t1;
+```
+
+Using the DISTINCT keyword for deduplication calculations, the mean standard error after removing duplicates [222.222, 3.3, 3.3, null] is 109.461.
+
+```text
++------------------------+
+| sem(distinct k_double) |
++------------------------+
+|                109.461 |
++------------------------+
+```
+
+### Error example
+
+```sql
+select sem(id) from t1;
+```
+
+```text
+ERROR 1105 (HY000): errCode = 2, detailMessage = sem only requires a double parameter: sem(id)
+```

i18n/zh-CN/docusaurus-plugin-content-docs/current/sql-manual/sql-functions/aggregate-functions/sem.md

@@ -0,0 +1,95 @@
+---
+{
+"title": "SEM",
+"language": "zh-CN"
+}
+---
+
+## 描述
+
+计算指定列或表达式的所有非 NULL 值的均值标准误。
+
+## 语法
+
+```sql
+SEM([DISTINCT] <expr>)
+```
+
+## 参数
+
+| 参数 | 说明 |
+| -- | -- |
+| `<expr>` | 是一个表达式或列，通常是一个数值列或者能够转换为数值的表达式，支持类型为 Double。|
+| `[DISTINCT]` | 是一个可选的关键字，表示对 expr 中的重复值进行去重后再计算均值标准误。 |
+
+## 返回值
+
+返回值为 Double。 返回所选列或表达式的均值标准误，如果组内的所有记录均为 NULL，则该函数返回 NULL 。
+
+## 举例
+
+```sql
+-- setup
+create table t1(
+        id int,
+        k_double double,
+) distributed by hash (id) buckets 1
+properties ("replication_num"="1");
+insert into t1 values 
+    (1, 222.222),
+    (2, 3.3),
+    (3, 3.3),
+    (4, null);
+```
+
+```sql
+select sem(k_double) from t1;
+```
+
+Double 类型的平均值计算，[222.222,3.3,3.3,null]的均值标准误为72.974。
+
+```text
++---------------+
+| sem(k_double) |
++---------------+
+|        72.974 |
++---------------+
+```
+
+```sql
+select sem(cast(null as double)) from t1;
+```
+
+值全为null时，返回null。
+
+```text
++---------------------------+
+| sem(cast(null as double)) |
++---------------------------+
+|                      NULL |
++---------------------------+
+```
+
+```sql
+select sem(distinct k_double) from t1;
+```
+
+使用 DISTINCT 关键字进行去重计算，[222.222,3.3,3.3,null]去重后均值标准误为109.461。
+
+```text
++------------------------+
+| sem(distinct k_double) |
++------------------------+
+|                109.461 |
++------------------------+
+```
+
+### 错误示例
+
+```sql
+select sem(id) from t1;
+```
+
+```text
+ERROR 1105 (HY000): errCode = 2, detailMessage = sem only requires a double parameter: sem(id)
+```

sidebars.json

@@ -1851,6 +1851,7 @@
                                 "sql-manual/sql-functions/aggregate-functions/regr-intercept",
                                 "sql-manual/sql-functions/aggregate-functions/regr-slope",
                                 "sql-manual/sql-functions/aggregate-functions/retention",
+                                "sql-manual/sql-functions/aggregate-functions/sem",
                                 "sql-manual/sql-functions/aggregate-functions/sequence-count",
                                 "sql-manual/sql-functions/aggregate-functions/sequence-match",
                                 "sql-manual/sql-functions/aggregate-functions/skew",