Deleting a datum affect SD
2013-06-03 8:29 pm
1. Suppose a datum is deleted from a set of data.
If the datum deleted is the mean or closer to the mean, then the new SD will increase. (Only exception: if all the data are the same, then the old SD is 0 and the new SD is unchanged.)
If the datum deleted is far from the mean, then the new SD will decrease.
2. Inserting a datum to a set of data
If the datum added is the mean or closer to the mean, then the new SD will decrease. (Only exception: if all the data are the same, then the old SD is 0 and the new SD is unchanged.)
If the datum added is far from the mean, then the new SD will increase.
Is it possible to prove the above theorems by using summation notation? Thanks.
回答 (2)
2013-06-08 8:54 pm
✔ 最佳答案
---------------------------------------------------------------------------------------------圖片參考：http://imgcld.yimg.com/8/n/HA05107138/o/20130608125353.jpg
2013-06-04 2:01 am
How far is far? Does it mean that the datum has greatest difference from the mean ( in terms of absolute value) ?
2013-06-03 18:02:32 補充：
i.e.
|X_1 - mean of {x_1,...,x_n} | >= |X_i - mean of {x_1,...,x_n}| for all i
in general
|X_1 - mean of {x_1,...,x_n} | > |X_j - mean of {x_1,...,x_n}| for some j
If the data are not all the same
2013-06-03 18:02:32 補充：
i.e.
|X_1 - mean of {x_1,...,x_n} | >= |X_i - mean of {x_1,...,x_n}| for all i
in general
|X_1 - mean of {x_1,...,x_n} | > |X_j - mean of {x_1,...,x_n}| for some j
If the data are not all the same
收錄日期: 2021-04-23 23:24:58
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20130603000051KK00116