考试原题求助

LaBellaVitaUID：3663517

set A (a,b,c,d,e)
set B (a+1, b+1, c+1,d+1,e+1)
两组数据的standard deviation作比较。题目好像说明abcde是consecutive integer。 在这中情况下是不是应该相等呢？如果不是consecutive integer，答案是不是无法判断呢？
谢谢各路高人

siuhonUID：3613947

Is there any change in the second case?
When i encounter this kind of question, i will try to key in random number.
If abcde are consecutive, say 1-5, the mean of this set of data would be 3 and mean of setB would be 4. As the 'distance' between each datum from the mean remains unchanged, i.e. 3-1=2 vs 4-2=2, SDs of two set are the same
I applied same strategy to the second case with 5 random numbers,{1,37,46,59,77}, giving the mean of 44 and mean of  the corresponding set b is 45.
the distance of each data set between mean and each datum is the same, 44-1 vs 45-2, thus, I conclude that the SD are still the same.

岳然UID：3654715

每个元素+1，那么平均值相对原来+1，平均值和每个元素的差值不变。元素数又没改变，那么标准差也没变。不需要是consecutive integer。

LaBellaVitaUID：3663517

岳然 发表于 2016-1-18 18:07
每个元素+1，那么平均值相对原来+1，平均值和每个元素的差值不变。元素数又没改变，那么标准差也没变。不需 ...

谢谢详解

LaBellaVitaUID：3663517

siuhon 发表于 2016-1-18 16:42
Is there any change in the second case?
When i encounter this kind of question, i will try to key i ...

谢谢您的解释，主要是考场没足够时间试，还是应该明白原理。