Prep-T1-DS 34

[w062611]

During an experiment, some water was removed from each of 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?

(1) For each tank, 30 percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.

(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.

答案為 A

小弟選C

高手可以指點一下小弟哪裡思路出了問題嗎

感謝指教

[little8]

頂一下,懇請數學高手解惑指教~~

[scottkidd]

這題主要就是考標準差的定義：(每一項與平均值的差)^2的總合再開根號，而通常AT都不太會考計算，所以主要的關鍵通常落在(每一項與平均值的差)這個關係上。

看兩個條件：
(1) For each tank, 30 percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
有each這個字，代表每一項跟平均值一起變動，那(每一項與平均值的差)勢必是沒有變的，所以標準差也不會改變，sufficient

(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.
只知道average的值，根本不知道(每一項與平均值的差)有沒有變，insufficient

[little8]

回覆相當清楚仔細,我懂了,感謝!!

[Huang Hsin-Yi]

這題主要就是考標準差的定義：(每一項與平均值的差)^2的總合再開根號，而通常AT都不太會考計算，所以主要的關鍵通常落在(每一項與平均值的差)這個關係上。

看兩個條件：
(1) For each tank, 30 percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
有each這個字，代表每一項跟平均值一起變動，那(每一項與平均值的差)勢必是沒有變的，所以標準差也不會改變，sufficient

我不懂這裡,我嘗試數字代,標準差是會隨著各項的多寡而不同,即便等比例
例如:
100,120 mean 110 則標準差為10
拿掉30%
70,84 mean 77 則標準差為7
我理解不對嗎?

(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.
只知道average的值，根本不知道(每一項與平均值的差)有沒有變，insufficient

[sunnyblue13s]

這題主要就是考標準差的定義原貼有誤，修正：(每一項與平均值的差)^2的總合...除以個數....再開根號，而通常AT都不太會考計算，所以主要的關鍵通常落在(每一項與平均值的差)這個關係上。

看兩個條件：
(1) For each tank, 30 percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
有each這個字，代表每一項跟平均值一起變動，那(每一項與平均值的差)勢必是沒有變的 - 這邊有誤；會變動，所以標準差也不會改變- 這邊有誤；會改變

我不懂這裡,我嘗試數字代,標準差是會隨著各項的多寡而不同,即便等比例
例如:
100,120 mean 110 則標準差為10
拿掉30%
70,84 mean 77 則標準差為7 ←-----很好的例子!!!

題目問的是一個"值".....所以....充分!!

(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.
只知道average的值，根本不知道(每一項與平均值的差)有沒有變，insufficient

[Huang Hsin-Yi]

結論:
也就是說 各項若一起減掉 30% ,則標準差也會一起減少 30%