diff --git a/fe/fe-core/src/main/java/org/apache/doris/analysis/ColumnDef.java b/fe/fe-core/src/main/java/org/apache/doris/analysis/ColumnDef.java
index 2c120243ac..3500f1bb97 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/analysis/ColumnDef.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/analysis/ColumnDef.java
@@ -126,6 +126,10 @@ public class ColumnDef {
         this(name, typeDef, false, null, false, DefaultValue.NOT_SET, "");
     }
 
+    public ColumnDef(String name, TypeDef typeDef, boolean isAllowNull) {
+        this(name, typeDef, false, null, isAllowNull, DefaultValue.NOT_SET, "");
+    }
+
     public ColumnDef(String name, TypeDef typeDef, boolean isKey, AggregateType aggregateType,
                      boolean isAllowNull, DefaultValue defaultValue, String comment) {
         this(name, typeDef, isKey, aggregateType, isAllowNull, defaultValue, comment, true);
diff --git a/fe/fe-core/src/main/java/org/apache/doris/catalog/InternalSchemaInitializer.java b/fe/fe-core/src/main/java/org/apache/doris/catalog/InternalSchemaInitializer.java
index 6dfc2e8ba0..3abaa3b8e6 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/catalog/InternalSchemaInitializer.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/catalog/InternalSchemaInitializer.java
@@ -159,8 +159,8 @@ public class InternalSchemaInitializer extends Thread {
         columnDefs.add(new ColumnDef("count", TypeDef.create(PrimitiveType.BIGINT)));
         columnDefs.add(new ColumnDef("ndv", TypeDef.create(PrimitiveType.BIGINT)));
         columnDefs.add(new ColumnDef("null_count", TypeDef.create(PrimitiveType.BIGINT)));
-        columnDefs.add(new ColumnDef("min", TypeDef.createVarchar(ScalarType.MAX_VARCHAR_LENGTH)));
-        columnDefs.add(new ColumnDef("max", TypeDef.createVarchar(ScalarType.MAX_VARCHAR_LENGTH)));
+        columnDefs.add(new ColumnDef("min", TypeDef.createVarchar(ScalarType.MAX_VARCHAR_LENGTH), true));
+        columnDefs.add(new ColumnDef("max", TypeDef.createVarchar(ScalarType.MAX_VARCHAR_LENGTH), true));
         columnDefs.add(new ColumnDef("data_size_in_bytes", TypeDef.create(PrimitiveType.BIGINT)));
         columnDefs.add(new ColumnDef("update_time", TypeDef.create(PrimitiveType.DATETIME)));
         String engineName = "olap";
diff --git a/fe/fe-core/src/main/java/org/apache/doris/statistics/ColumnStatistic.java b/fe/fe-core/src/main/java/org/apache/doris/statistics/ColumnStatistic.java
index 3dfc66adbd..f753201cf3 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/statistics/ColumnStatistic.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/statistics/ColumnStatistic.java
@@ -147,10 +147,14 @@ public class ColumnStatistic {
             if (!StatisticsUtil.isNullOrEmpty(min)) {
                 columnStatisticBuilder.setMinValue(StatisticsUtil.convertToDouble(col.getType(), min));
                 columnStatisticBuilder.setMinExpr(StatisticsUtil.readableValue(col.getType(), min));
+            } else {
+                columnStatisticBuilder.setMinValue(Double.NaN);
             }
             if (!StatisticsUtil.isNullOrEmpty(max)) {
                 columnStatisticBuilder.setMaxValue(StatisticsUtil.convertToDouble(col.getType(), max));
                 columnStatisticBuilder.setMaxExpr(StatisticsUtil.readableValue(col.getType(), max));
+            } else {
+                columnStatisticBuilder.setMinValue(Double.NaN);
             }
             columnStatisticBuilder.setSelectivity(1.0);
             columnStatisticBuilder.setOriginalNdv(ndv);