[問題] 合併群組變異數的問題
Sample 1 consists of 4 individuals, and the sample mean = 50K, and the sample
standard deviation = 10K.
Sample 2 consists of 8 individuals, and the sample mean = 50K, and the sample
standard deviation = 5K.
Now you want to merge the two samples to obtain the sample mean and the sample
standard deviation of the merged sample of 12 individuals. What are the
sample mean and the sample standard deviation of the merged sample?
(Hint: What is the definition of sample variances?)
a. Sample mean = 50K, sample stdev = 15K
b. Sample mean = 50K, sample stdev = 6.571K
c. Sample mean = 100k, sample stdev = 15K
d. Sample mean = 50K, but insufficient information is given for the sample
standard deviation.
e. Sample mean = 50K, sample stdev = 11.18K
可是我算出來的答案是7.0711(以上皆非)
我的算法
variance1 = 1/4 [ SUM (X_1i- 50)^2] = 100
variance2 = 1/8 [ SUM (X_2i- 50)^2] = 25
variance 1&2 = 1/12 [SUM (X_1i- 50)^2 + SUM (X_2i- 50)^2]
= 50
stdev = 7.0711
這樣的想法哪裡錯了
謝謝指教
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