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作者: kissinwang (★兔兔世界的王子★) 看板: Wanted
標題: Re: [問題] 數學一題
時間: Fri Jul 20 05:49:27 2012

Stmt I
Let h be the highest number
Let the median be the middle number
Let l be the lowest number

h-l = 2(h-median)
h-l = 2h-2median

2median = h+l

median = (h+l)/2 (1)

mean = l+median+h/3

3 mean = l+h+median

3mean = l+ h + (l+h)/2

6 mean = 3(l+h)

mean = l+h/2 (2)

From (1) and (2) mean and median are the same

SUFF

Stmt II

Let 3 numbers be x,y,z

3x= x+y+z i.e 2x = y+z i.e x = y+z/2

(Or)

y = x+z/2 (similar to above)

(or)

z = x+y/2

Again this is telling us that there is a common difference between one number
to the next number and is is the same SINCE ONE OF THE NUMBERS THAT FALLS
EXACTLY BETWEEN 2 OTHERS NUMBERS IS THE AVERAGE OF THE 2 NUMBERS

Mean = Median (for consecutive numbers or for numbers where the common
difference is the same from one number to thenext after arranging them in
ascending order)


※ 引述《chenemily (天天保持好心情)》之銘言：
: A certain list consists of 3 different numbers. Does the median of the 3
: numbers equal the average (arithmetic mean) of the 3 numbers?
: 請問一下 從題意
: 可以知道3個數是等差嗎
: 因為解答的寫法 讓我看不太懂
: 我只是設有3個數 A<B<C
: The sum of the 3 numbers is equal to 3 times one of the numbers.
: 然後題目問上面陳述 是否陳立
: 有數學達人來解答一下
: 謝

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→ kissinwang:我的資質只可以理解這版本~~你那版本我也不懂~攤 07/20 05:50
推 chenemily:O很謝謝拉 GOOGLE我也會阿 但是就不太懂阿 07/20 05:51
→ kissinwang:median = b and average is (a+b+c)/3 他多了這個~~ 07/20 05:52
→ kissinwang:然後導到最後也只可以確定2b=c+a 但你問的題目是說 07/20 05:55
→ kissinwang:a+b+c=3a或3b或3c...頂多等於3b而已~所以不得証 07/20 05:56
推 chenemily:我就是想知道為啥3A 或3C不可以 07/20 05:56
→ kissinwang:因為只有b是中間數~~攤 07/20 06:19
→ catcookie27:我怎麼覺得題目根本就沒說是不是等差 07/20 07:08
推 melomelomelo:題目沒說明是不是等差 兩個問題都是問號 沒有陳述 07/20 07:34
→ melomelomelo:並不是三個不同的數字 就一定是等差 07/20 07:35
→ melomelomelo:原原PO應該漏了一些東西 沒有寫出來 07/20 07:37
→ chenemily:沒有喔 題目就真的這樣而已 07/20 08:44