一组学生在一次实验中使用量筒记录了水的体积。记录的水体积平均值为 1.8 cm3，标准差为 0.28 cm3。老师点出所有学生的读数都存在误差。所有学生在视线平视时记录的读数都比正确读数高了 0.6 cm3。解释该误差是如何影响正确的水体积平均值和标准差的。

它不会直接告诉你答案，而是问你卡在哪一步看看 AI 是怎么陪你一步步弄懂这道题的

完整解法

1. Correct the mean by subtracting the common error from every recorded value.

Each recorded reading is $0.6\text{ cm}^3$ above the correct reading.

So the correct mean is
$1.8-0.6=1.2\text{ cm}^3.$

2. State the effect on the standard deviation.

Since every reading is reduced by the same amount, the distances of the readings from their mean are unchanged.

Therefore, the standard deviation is unchanged:
$0.28\text{ cm}^3.$

答案

The correct mean volume is $1.2\text{ cm}^3$ .

The standard deviation is unchanged, so it remains $0.28\text{ cm}^3$ .

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