Course: 4.6 计算百分比错误-interactive

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计算百分比错误

Error in Measurements
::测量中的错误

Percent error is a concept that is seen in situations of measurement . C ommon examples include polling and physical measurements.
::百分率误差是衡量情况中看到的概念,常见的例子包括投票和实物测量。

Use the ruler to find the length of the object below.
::使用标尺查找下面对象的长度。

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Which of the following units would be a more exact measurement.
::以下哪些单位将是一个更精确的计量方法。

Discussion Questions
::讨论问题讨论问题

What challenges were presented in the interactive above?
::上述互动中提出了哪些挑战?

Was your measurement accurate? Why or why not?
::测量是否准确?

How can we measure how far away from the actual value our measurement was?
::我们如何衡量距离我们衡量的实际价值有多远?

Is it possible to get a perfectly accurate measurement?
::有没有可能得到一个非常准确的测量?

Absolute Error
::绝对错误

Every measurement has an error. But the question is, how much error does the measurement have?
::每个测量都有一个错误。但问题是,测量有多少错误?

Imagine a clock is off by one tenth of a second each second. A tenth of a second does not sound like a big error. H owever, because there are so many seconds in a year, the error becomes gigantic over time. In fact, it would be over a month late at the end of the year!
::想象一下时钟每秒关闭十分之一。时钟每秒关闭十分之一。时钟每秒的十分之一听起来不像大错误。但是, 由于每年有这么多秒, 错误会随着时间而变得巨大。事实上, 年终时会迟到一个多月 !

Small errors can have a large effect when projected over a large scale. The error in measurement can be calculated by subtracting it from a known measurement that is widely considered accurate.
::如果对大尺度进行预测,小误差可能会产生很大影响。测量中的误差可以通过从广泛认为准确的已知误差中减去来计算。

\begin{aligned} Absolute Error = |Actual Value - Measured Value| \end{aligned}

$\begin{align*}\textrm{Absolute Error = |Actual Value - Measured Value|}\end{align*}$
::绝对错误 = 实际值 - 测量值

Recall that absolute value can be used to measure the distance between two values. In this case, you want to find the distance between the measured value and the actual value .
::回顾绝对值可用于测量两个值之间的距离。在此情况下,您要找到测量值与实际值之间的距离。

Use the interactive below to review absolute value.
::使用下面的交互数据来审查绝对值。

Example
::示例示例示例示例

Sarah is testing the accuracy of a scale in her chemistry lab. She took a weight which she knew has a mass of 20 kg and weighed it. The scale read that the weight weighed 20.4 kg. What is the absolute error of the mass of the weight that Sarah recorded?
::Sarah正在化学实验室测试一个比例尺的准确性。她拿了一个她知道质量为20公斤的重量来称重。比例尺读出体重为20.4公斤。 Sarah所记录的重量质量的绝对误差是多少?

U se the absolute error formula to determine this.
::使用绝对错误公式来确定此值。

$\begin{align*}\textrm{Absolute Error = |Actual Value - Measured Value|}\end{align*}$
::绝对错误 = 实际值 - 测量值

Absolute Error: x
::绝对误差: x

Actual Value: 20
::实际价值:20

Measured Value: 20.4
::计量值:20.4

$\begin{align*}x &= |20 - 20.4| \\ x &= |-0.4| \\ x &= 0.4\end{align*}$
::x20-20.4x0.4x=0.4

Answer: The absolute error was 0.4 kg.
::答复:绝对误差为0.4公斤。

Use the interactive below to find the absolute error from your measurements.
::使用下面的交互数据从测量中找到绝对错误。

ercent-problems" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f457782df64f5d4be7a6306&collectionHandle=algebra&collectionCreatorID=3&conceptCollectionHandle=algebra-:

ercent-problems&mode=lite" test-id="5f457782df64f5d4be7a6306">

Discussion Question
::讨论问题

What is the purpose of the absolute value in absolute error?
::绝对误差绝对值的目的是什么?

Percent Error
::百分比错误

If you are trying to measure the length of an object and are off by 1 centimeter, what does this mean? Was it an accurate or inaccurate measurement?
::如果试图测量物体的长度,但关闭1厘米,这意味着什么?这是准确的还是不准确的测量?

The answer depends on the scale of what you were measuring. If you measured the width of a quarter, it was likely an inaccurate measurement. If you measured the length of a bridge, it was likely an accurate measurement.
::答案取决于您测量的大小。如果您测量了四分之一的宽度, 它很可能是一个不准确的测量。如果您测量了桥梁的长度, 它很可能是一个准确的测量。

You can quantify the relationship between the absolute error and the actual value by using the percent error.
::您可以使用百分比错误来量化绝对错误与实际值之间的关系。

\begin{aligned} Percent Error = \frac{|Actual Value - Measured Value|}{Actual Value} \cdot 100 \end{aligned}

$\begin{align*}\textrm{Percent Error} = \frac{\textrm{|Actual Value - Measured Value|}}{\textrm{Actual Value}} \cdot 100\end{align*}$
::百分比错误实际值 - 测量值实际值 100

This formula will return the absolute error as a percentage of the actual value. This value will allow us to determine if the error is relatively large or relatively small.
::此公式将返回绝对误差占实际值的百分比。此值将允许我们确定误差是相对较大还是相对较小。

Example
::示例示例示例示例

In the previous example, Sarah received a measurement of 20.4 kg when measuring a 20 kg weight. What is the percent error of her measurement?
::在前一个例子中,Sarah在测量20公斤重量时,得到20.4公斤的测量。测量的百分率误差是多少?

Percent Error: x
::百分比错误: x

Actual Value: 20
::实际价值:20

Measured Value: 20.4
::计量值:20.4

$\begin{align*}x &= \frac{|20 - 20.4|}{20} \cdot 100 \\ x &= \frac{|-0.4|}{20} \cdot 100 \\ x &= \frac{0.4}{20} \cdot 100 \\ x &= 0.02 \cdot 100 \\ x &= 2\end{align*}$
::x20-20.420_100x_0.420_100x=0.420_100x=0.02_100x=2

Answer: The percent error was 2% which means that the scale will be off by 2% over the actual mass.
::回答:百分比错误为2%,这意味着比重将比实际质量减少2%。

Use the interactive below to practice finding percent error.
::使用下面的交互操作来练习查找% 错误。

ercent-of-change" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f457765134573bd98ef1166&collectionHandle=arithmetic&collectionCreatorID=3&conceptCollectionHandle=arithmetic-:

ercent-of-change&mode=lite" test-id="5f457765134573bd98ef1166">

Summary

Find the absolute error using the equation: $\begin{align*}\text{absolute error}=\left|\text{actual value}-\text{measured value}\right|\end{align*}$

::使用方程式查找绝对错误 : 绝对错误 ======================================================================================================================================================================================== = ===== === = = ====== = = ======= == = = = ===== = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

Find percent error using the equation: $\begin{align*}\text{percent error}=\frac{\left|\text{actual value}-\text{measured value}\right|}{\text{actual value}}\times100\end{align*}$
::使用方程式查找% 错误:% 错误:% 实际值 - 测量值=% 实际值×100

Section outline

General

计算百分比错误

Error in Measurements ::测量中的错误

Absolute Error ::绝对错误

Percent Error ::百分比错误

Error in Measurements
::测量中的错误

Absolute Error
::绝对错误

Percent Error
::百分比错误