standard deviation一問

mean (平均數) , standard deviation (標準差)
variance (方差)

e.g. 1, 3, 5, 7, 9

mean
=sum of data / number of data
= (1+3+5+7+9) / 5
= 25/ 5
= 5

standard deviation
= square root of variance

variance
= (1/N * sum of square of data) - square of mean
= [1/5 * (1² + 3² + 5² + 7² + 9²)] - 5²
=[1/5 * (1 + 9 + 25 + 49 + 81)] - 25
=(1/5 * 165) - 25
=33 - 25
=8
(N menas number of data)

standard deviation (標準差)
=square root of variance
=square root of 8
=2.8284 (to 4 d. p.)

“Given 一堆data個 mean 同 standard deviation
之後 改一個data, mean 改變左, 點計個新standard deviation” ?

example as follow :

Given : {1, 3, 5, 7, 9}
mean is 5
standard deviation is 2.8284 (to 4 d. p.)

改一個data (change a data)
new set of data {1, 3, 6, 7, 9}

mean
= sum of data / number of data
= (1 + 3 + 6 + 7 + 9) / 5
= 5.2

variance
=[ 1/ N * (sum of square of data)] - square of mean
=[ 1/ 5 * (1² + 3² + 6² + 7² + 9²)] - (5.2)²
=(1/ 5 * 176) - 27.04
= 8.16

standard deviation
= square root of variance
= square root of 8.16
= 2.8566 (to 4 d. p.)


given a set of data,
to calculate standard deviation (標準差)

formula (公式) as follow :

standard deviation
= square root (平方根) of variance (方差)

(which) variance is
(1/N * sum of square of data) - mean²


hope it is useful

2006-11-17 15:58:07 補充：
“知道一堆data個mean同standard deviation之後改一個data, mean改變左, 咁點計個新standard deviation” ?your question is not clearsuppose we known a group of data's - mean- standard deviation- number之後改一個data, suppose we know the changed data (old one & new one)

2006-11-17 15:59:15 補充：
example as follow :Given : a groud of data's - mean is 5- standard deviation is 2.8284 (to 4 d. p.)- number is 5 改一個data (change a data)change it to 6 (the old one is 5)

2006-11-17 16:01:16 補充：
(suggestion solution) new mean= sum of data / number of data= (5 * 5 - 5 + 6) / 5= 5.2 variance =[ 1/ N * (sum of square of data)] - square of mean={ 1/ 5 * [(2.82842 + 52)5 - 52 + 62] } - (5.2)2 = 8.16

2006-11-17 16:05:33 補充：
standard deviation= square root of variance= square root of 8.16= 2.8566 (to 4 d. p.) (I am a student who is studying Maths. & Sta.It is a great idea if you can provide a completed question 完整的問題 which is 用作 學術交流)

答得好好呀, 又清楚!