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`Algorithmic Knowledge` Average

2022-08-06 17:27:00Su Pimo

Average properties

添加一个

A set of numbers is knownS, 其平均值为avg.
Now in the collection, number of rejoinsx, Let the mean of the new set be avgg

则:
若 x < a v g , 有 : x < a v g g < a v g 若 x = a v g , 有 : a v g g = a v g 若 x > a v g , 有 : a v g < a v g g < x 若x < avg, 有: x < avgg < avg \\ 若x = avg, 有: avgg = avg \\ 若x > avg, 有: avg < avgg < x \\ x<avg,:x<avgg<avgx=avg,:avgg=avgx>avg,:avg<avgg<x

添加一个

A set of numbers is knownS, 其平均值为avg.
Now from the collection, 删除某个数x, Let the mean of the new set be avgg

则:
若 x < a v g , 有 : a v g g > a v g 若 x = a v g , 有 : a v g g = a v g 若 x > a v g , 有 : a v g g < a v g 若x < avg, 有: avgg > avg \\ 若x = avg, 有: avgg = avg \\ 若x > avg, 有: avgg < avg \\ x<avg,:avgg>avgx=avg,:avgg=avgx>avg,:avgg<avg

添加多个

A set of numbers is knownS, 其平均值为avg.
Now in the collection, Add some more numbers (这些数的平均值为avg1), Let the mean of the new set be avgg

Actually it can be: Several were added individuallyavg1

则:
若 a v g 1 < a v g , 有 : a v g 1 < a v g g < a v g 若 a v g 1 = a v g , 有 : a v g g = a v g 若 a v g 1 > a v g , 有 : a v g < a v g g < a v g 1 若avg1 < avg, 有: avg1 < avgg < avg \\ 若avg1 = avg, 有: avgg = avg \\ 若avg1 > avg, 有: avg < avgg < avg1 \\ avg1<avg,:avg1<avgg<avgavg1=avg,:avgg=avgavg1>avg,:avg<avgg<avg1

删除多个

A set of numbers is knownS, 其平均值为avg.
Now from the collection, 删除若干个数 (这些数的平均值为avg1), Let the mean of the new set be avgg

Actually it can be: Several were deleted individuallyavg1

则:
若 a v g 1 < a v g , 有 : a v g g > a v g 若 a v g 1 = a v g , 有 : a v g g = a v g 若 a v g 1 > a v g , 有 : a v g g < a v g 若avg1 < avg, 有: avgg > avg \\ 若avg1 = avg, 有: avgg = avg \\ 若avg1 > avg, 有: avgg < avg \\ avg1<avg,:avgg>avgavg1=avg,:avgg=avgavg1>avg,:avgg<avg

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