d = df.groupby('Item_Identifier')['Sales'].mean().to_dict()
print (d)
{'Beef': 3030.0, 'Milk': 1233.3333333333333, 'Tea': 150.0}

print (df['Item_Identifier'].map(d))
0    1233.333333
1    1233.333333
2    1233.333333
3    3030.000000
4    3030.000000
5     150.000000
6     150.000000
7     150.000000
Name: Item_Identifier, dtype: float64

bins = [df['Sales'].min(),500, 1500, df['Sales].max()]
labels=['low','medium','high']
df['Price Category'] = pd.cut(df['Item_Identifier'].map(d), bins=bins, labels=labels)
print (df)
  Item_Identifier  Sales Price Category
0            Milk    500         medium
1            Milk   1200         medium
2            Milk   2000         medium
3            Beef     60           high
4            Beef   6000           high
5             Tea    150            low
6             Tea    100            low
7             Tea    200            low