Question

Short Version:
Can StdDevs be added/combined? i.e.

if StdDev(11,14,16,17)=X and StdDev(21,34,43,12)=Y  
can we calculate StdDev(11,14,16,17,21,34,43,12) from X & Y

Long Version:
I am designing a star schema. The schema has a fact_table (grain=transaction) which stores individual transaction response_time. The schema also has an aggregate_table (grain=day) which stores the response_time_sum per day.
In my report I need to calculate standard deviations of the response time for a given timedimension, say day, week, month etc. How can I calculate the StandardDeviation using the aggregate_table instead of touching the huge fact_table?

Answer 1

是的,你可以把它们结合起来。你们需要了解观察次数、含义和标准偏差。差异比标准偏差更容易工作,因此我只字不提差异。 (标准偏差被定义为差异的正本。)

表示：

n[i] # observations for day i
m[i] # mean for day i
v[i] # variance for day i

页: 1 这容易:

days = [day1, day2, ..., day_final]
N = sum(n[i] for i in days)
M = sum(n[i] * m[i] for i in days) / N

The overall variance V is more complicated, but still can be calculated:

s1 = sum(n[i] * v[i] for i in days)
s2 = sum(n[i] * (m[i] - M)**2 for i in days)
V = (s1 + s2) / N

以上是人口差异。如果您有<代码>v[i]作为样本差异,则需要对<代码>1和<编码>进行一些小改动:

s1_sample = sum((n[i] - 1) * v[i] for i in days)
V_sample = (s1_sample + s2) / (N - 1)

Answer 2

无,你可以补充标准偏差。

随函附上你提供的数字:

X = 2.645751311, Y = 13.72345923

Standard deviation of combined set: 11.48912529

你们可以使用标准偏离公式作更一般性的证明。你们需要二者的共同点,即:

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