请问思路

qiqi

7根绳子，MEAN=68，MEDIAN=84，最长的是最短的的四倍再加14，问最长的长度范围，[em12]

tongxun

84-134
a1、a2、a3、a4、a5、a6、a7
a4=84
a5=a6=a7=a4=84

a5=a6=a4=84；a1=a2=a3 =》134

qiqi

多谢！明白

cranberry

请老大详细解释一下，拜托

likerock

My answer is that the longest is between 70 and 134.

Assume the order is a1, a2, a3, a4, a5, a6, a7.  We know a4 is 84.  We also know a7=4*a1+14.  The largest number a7 could have is when the other numbers are the possible lowest, which means a2, a3 = a1 and a5, a6 = 84.  Same reason, the smallest number a7 could have is when the other numbers are the possible biggest, which means a2, a3 = 84 and a5, a6 = a7.  Since we know mean is 68, so the sum is 476.  We can get following equations.

1.  3*a1 + 84*3 + a7 = 476 for biggest number
2. a1 + 84*3 + 3*a7 = 476 for smallest number
3. a7 = 4*a1 + 14 (this is we already know)

from above we can calculate that the a7 is between 70 and 134.

Hope it helps.

qiqi

likerock，最长的长度最小值不可能是70，最长值是70的话，中数怎么可能是84，因为中数的定义是按大小排列的。

likerock

Oops, you're right, qiqi.  I forget another hidden premise a7 >= 84.  Thanks for correcting me.

cranberry

thank you ,guys