如何使用 BigQuery 计算几何平均值，同时考虑样本中每个项目的权重？

Question

我知道如何通过 this post 使用 EXP(AVG(LN(x))) 计算地理平均值。这非常有帮助。现在我需要计算几何平均值，同时考虑样本中每个项目的重量。

代数表达式看起来像这样

所以我的问题是如何在 BigQuery 中计算它？以及如何考虑每件物品的重量有什么建议吗？

示例数据

SELECT STRUCT(JSON_EXTRACT_SCALAR(mass, '$.subs_sum') AS subs, JSON_EXTRACT_SCALAR(mass, '$.division') AS division) mass  FROM UNNEST (
    [
        '''{
            "subs_sum": "188292",
            "division": "0.7708596151869399"
        }''',
        '''{
            "subs_sum": "1182",
            "division": "0.8344408128719736"
        }''',
        '''{
            "subs_sum": "142559",
            "division": "0.9539818702339475"
        }''',
        '''{
            "subs_sum": "14047",
            "division": "0.7836811141666864"
        }''',
        '''{
            "subs_sum": "70344",
            "division": "0.7724158684628387"
        }''',
        '''{
            "subs_sum": "101516",
            "division": "0.8676896770665041"
        }''',
        '''{
            "subs_sum": "12459",
            "division": "0.8029440607145902"
        }''',
        '''{
            "subs_sum": "26070",
            "division": "0.9793106723267602"
        }''',
        '''{
            "subs_sum": "151959",
            "division": "0.839048212451375"
        }''',
        '''{
            "subs_sum": "5234",
            "division": "0.684263034290403"
        }'''
    ]
) mass

Answer 1

你问题中的公式相当于下面一个

可以很容易地按照下面的示例进行编码

select exp(sum(mass.subs * ln(mass.division)) / sum(mass.subs ))
from data

如果应用于您问题中的示例数据

with data as (
  SELECT STRUCT(
    cast(JSON_EXTRACT_SCALAR(mass, '$.subs_sum') as float64) AS subs, 
    cast(JSON_EXTRACT_SCALAR(mass, '$.division') as float64) AS division
    ) as mass  
  FROM UNNEST ([
  '{"subs_sum": "188292","division": "0.7708596151869399"}',
  '{"subs_sum": "1182","division": "0.8344408128719736"}',
  '{"subs_sum": "142559","division": "0.9539818702339475"}',
  '{"subs_sum": "14047","division": "0.7836811141666864"}',
  '{"subs_sum": "70344","division": "0.7724158684628387"}',
  '{"subs_sum": "101516","division": "0.8676896770665041"}',
  '{"subs_sum": "12459","division": "0.8029440607145902"}',
  '{"subs_sum": "26070","division": "0.9793106723267602"}',
  '{"subs_sum": "151959","division": "0.839048212451375"}',
  '{"subs_sum": "5234","division": "0.684263034290403"}'
  ]) mass 
)
select exp(sum(mass.subs * ln(mass.division)) / sum(mass.subs ))
from data

输出是

如何使用 BigQuery 计算几何平均值，同时考虑样本中每个项目的权重？

How to calculate the geometric mean, taking into account the weight for each item in the sample using BigQuery?

google-bigquery

mean

algebra