课程： 1.4 定序实际数字和绝对值

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排序实际数字和绝对值

When most people go to the meat counter at a grocery store, they order by describing what fraction of a pound they want. For example, say $\begin{aligned} \frac{1}{4} \end{aligned}$ of a pound. However, the butcher measures the meat on a scale that uses a decimal number. If the butcher measures out 0.3 pounds, has he measured out too much, not enough, or the correct amount?
::当大多数人去一家杂货店的肉食柜台时, 他们通过描述他们想要的一磅的分量来订购。例如, 比如说一磅的14磅。但是, 屠夫用小数数来测量肉类。如果屠夫用0.3磅衡量, 他是否衡量得过高, 不足够, 或数量正确?

In this section, we review how to compare the size of numbers.
::在本节中,我们审查如何比较数字大小。

Inequality Symbols
::不平等符号

The table below lists the inequality symbols, what they mean, and examples.
::下表列出了不平等符号、它们的含义和实例。

Less Than
::小于

Symbol: $\begin{aligned} < \end{aligned}$
::符号: <

Example: $\begin{aligned} 3 < 4 \end{aligned}$
::示例:3 < 4

Verbal: less than, is under, is fewer than
::口音:小于, 低于, 低于, 低于, 低于, 低于

Greater Than
::大宽

Symbol: $\begin{aligned} > \end{aligned}$
::符号: >

Example: $\begin{aligned} 4 > 3 \end{aligned}$
::示例:4>3

Verbal: greater than, is more than, is over, exceeds
::口音:大于,多于,超过,超过,超过,超过

Less Than or Equal to
::小于或等于

Symbol: $\begin{aligned} \leq \end{aligned}$
::文号:___________________________________________________________

Example: $\begin{aligned} 3 \leq 4 or 4 \leq 4 \end{aligned}$
::示例:34或44

Verbal: less than or equal to, is at most, is not greater than, does not exceed, is not more than
::语言:小于或等于、最多等于、最多等于、不超过、不超过、不超过、不超过、不超过

Greater Than or Equal to
::大于或等于

Symbol: $\begin{aligned} \geq \end{aligned}$
::文号:___________________________________________________________

Example: $\begin{aligned} 4 \geq 3 or 4 \geq 4 \end{aligned}$
::示例:4 3或4 4

Verbal: greater than or equal to, is at least, is not less than, is not under
::语言:大于或等于,至少,不小于,不低于,不低于

To compare the size of numbers, it is best to consider them in decimal form by comparing their place values.
::为了比较数字的大小,最好通过比较其地点值来考虑小数点后的数字。

by Mathispower4u explains how to determine the types of real numbers, compare and , and determine the absolute value of a real number .
::使用 Mathispower4u 来解释如何确定真实数字的类型、比较和以及确定真实数字的绝对值。

Place Value
::位值

The real number system is a base 10 number system. Each place value represents a power of 10.
::实际数字系统是基数 10 的系统。每种地点值的功率为 10 。

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

Tenths

Hundredths

Thousandths

$\begin{aligned} 10^{5} = \end{aligned}$

$\begin{aligned} 100, 000 \end{aligned}$

$\begin{aligned} 10^{4} = \end{aligned}$

$\begin{aligned} 10, 000 \end{aligned}$

$\begin{aligned} 10^{3} = \end{aligned}$

$\begin{aligned} 1, 000 \end{aligned}$

$\begin{aligned} 10^{2} = \end{aligned}$

$\begin{aligned} 100 \end{aligned}$

$\begin{aligned} 10^{1} = \end{aligned}$

$\begin{aligned} 10 \end{aligned}$

$\begin{aligned} 10^{0} = \end{aligned}$

$\begin{aligned} 1 \end{aligned}$

$\begin{aligned} 10^{- 1} = \end{aligned}$

$\begin{aligned} 0.1 \end{aligned}$

$\begin{aligned} 10^{- 2} = \end{aligned}$

$\begin{aligned} 0.01 \end{aligned}$

$\begin{aligned} 10^{- 3} = \end{aligned}$

$\begin{aligned} 0.001 \end{aligned}$

We can use the place values in the decimal form of each number to compare their sizes, even if they are different types of real numbers.
::我们可以使用每个数字小数点的位值来比较其大小,即使它们是不同类型的实际数字。

Example 1
::例1

Say you order $\begin{aligned} \frac{1}{4} \end{aligned}$ of a pound of turkey. However, the butcher measures the meat on a scale that uses a decimal. If the butcher measures out 0.3 pounds, is that correct? Is it too much or too little?
::说您订购了14磅火鸡。然而,屠夫用小数点来测量肉类的大小。如果屠夫用0.3磅来测量肉类,这是否正确?是太多还是太少?

Solution: Let's divide 4 into 1 to determine what $\begin{aligned} \frac{1}{4} \end{aligned}$ is as a decimal. We have $\begin{aligned} \frac{1}{4} \end{aligned}$ = 0.25.
::解决办法:让我们将4分为1,以确定14是小数。我们有14=0.25。

Now, that we have two decimals we can compare them by place value. We work from left to right considering the larger place values first. There is a 2 in the tenths place in 0.25 and a 3 in the tenths place of 0.3. Therefore , 0.25 < 0.3. The butcher has measured out too much turkey.

::现在,我们有两个小数点, 我们可以按位数来比较它们。我们从左到右首先考虑更大的位数。 0. 25是十分之一, 0. 3是十分之一。因此, 0. 25 < 0. 3。屠夫测量了太多的火鸡。

Example 2
::例2

List $\begin{aligned} \frac{3}{4}, 1.23, \sqrt{2}, \frac{2}{3}, 1 \end{aligned}$ and $\begin{aligned} \frac{8}{7} \end{aligned}$ in order from least to greatest.
::名单341.23、2、33、1和87,从最少到最多顺序。

Solution: First, write each number as a decimal.
::解答: 首先, 将每个数字以小数表示。

\begin{aligned} \frac{3}{4} = 0.75 & 1.23 \\ \sqrt{2} = 1.4142... & \frac{2}{3} = 0.6 \bar{6} \\ 1 & \frac{8}{7} = 1. \bar{142857} \end{aligned}

Next, we compare the place values working from left to right, or largest place value to smallest place value. 1.23, $\begin{aligned} \sqrt{2} \end{aligned}$ , 1, and $\begin{aligned} \frac{8}{7} \end{aligned}$ all have a 1 in the ones place, so they are larger than $\begin{aligned} \frac{3}{4} \end{aligned}$ and $\begin{aligned} \frac{2}{3} \end{aligned}$ . $\begin{aligned} \frac{2}{3} \end{aligned}$ is smaller than $\begin{aligned} \frac{3}{4} \end{aligned}$ because the 6 in the tenths place is smaller than the 7. These are the first two numbers in our list.
::接下来,我们比较从左到右工作的位置值,或最大的位置值,到最小的位置值。 1.23, 2, 1, 和 87 都有一个位置, 所以它们大于34, 23, 23小于34, 因为十分位的6比7小。这些是我们清单上的前两个数字。

The smallest among the remaining four numbers is 1, since 1=1.0 and the 0 in the tenths place is smaller than the remaining numbers.
::其余四个数字中最小的为1,自1=1.0以来为1,十分之一的0比其余数字小。

Comparing the tenths places of the remaining three numbers, we have $\begin{aligned} \frac{8}{7} < 1.23 < \sqrt{2} \end{aligned}$ since 1 < 2 < 4 in the tenths place.
::与其余三个数字的十分之一位相比,我们共有87个 <1.23 < 2位,自第十位1 < 2 < 4位以来。

The final list in order is then : $\begin{aligned} \frac{2}{3}, \frac{3}{4}, 1, \frac{8}{7}, 1.23, \sqrt{2} \end{aligned}$
::最后名单依次为:23 341 87 1.23,2

Example 3
::例3

Replace the blank between $\begin{aligned} - \frac{5}{3} \end{aligned}$ ______ $\begin{aligned} - \frac{π}{2} \end{aligned}$ with <, > or =.
::将 - 53 2 之间的空白替换为 < 、 > 或 = 。

Solution: Be careful! For negative numbers, numbers that are closer to zero on the number line are larger.
::解决方案: 小心点! 对于负数, 数字线上接近零的数字更大。

First, we write both numbers in decimal form. $\begin{aligned} - \frac{5}{3} = - 1.6 \bar{6}, - \frac{π}{2} \approx - 1.57079 \end{aligned}$ . 1.5 is closer to zero than 1.6. This means that $\begin{aligned} - \frac{π}{2} \end{aligned}$ is the larger number, so $\begin{aligned} - \frac{5}{3} < - \frac{π}{2} \end{aligned}$ .
::首先,我们以小数形式写下两个数字。 -531.66,21.57079。 1.5比1.6接近零。这意味着%2是最大的数字,所以~532。

by Mathispower4u provides an example of listing five decimals in order from least to greatest.
::依据 Mathispower4u 提供一个例子,列出从最小到最大的五小数顺序。

Example 4
::例4

List $\begin{aligned} - \frac{1}{4}, \frac{3}{2}, - \sqrt{3}, \frac{3}{5} \end{aligned}$ , and 2 in order from greatest to least.
::清单14、32、-3、35和2,从最大到最低顺序。

Solution: First, w rite all the numbers as decimals. $\begin{aligned} - \frac{1}{4} = - 0.25, \frac{3}{2} = 1.5, - \sqrt{3} \approx - 1.732, \frac{3}{5} = 0.6, 2 \end{aligned}$ . The positive numbers are greater than the negative numbers, so we will list them first: 2 > 1.5 > 0.6.
::解决方案 : 首先, 将所有数字都写成小数数。 - 140. 25, 32=1.5, - 31. 732, 35=0. 6 2。正数大于负数, 所以我们先列出2 > 1. 5 > 0. 6。

Comparing the negative numbers, 0.25 is closer to zero than 1.732. Therefore, -0.25 is greater than -1.732.
::与负数相比,0.25比1.732接近零。因此,-0.25大于-1.732。

In conclusion, the order of the numbers from greatest to least are: $\begin{aligned} 2, \frac{3}{2}, \frac{3}{5}, - \frac{1}{4}, - \sqrt{3} \end{aligned}$
::总而言之,从最大到最低数字的顺序是:2,32,35,-14,-3。

WARNING
::警告

Negative numbers are larger when they are closer to zero .
::当负数接近零时,负数会更大。

In the context of money and temperature, this makes sense. In the previous example, we compared -0.25 and -1.73. If we think of these numbers as money, you have more money if you only owe $0.25 than if you owe $1.73. So, -0.25 > -1.73. In the context of temperature, -3°C is a warmer temperature than -10°C.
::在货币和温度方面,这是有道理的。在上一个例子中,我们比较了 -0.25和-1.73。如果我们把这些数字当作货币,那么,如果你只欠2.25美元,那么你的钱就会比欠1.73美元多。那么,在温度方面, -0.25 > -1.73。在温度方面, -3°C是比 -10°C更温暖的温度。

Absolute Value
::绝对值

Absolute value is the distance of a number from zero on the number line. Since it measures distance, it is always a positive number or zero. (To remember this, note no one goes to the store and asks for -8 feet of lumber or -2 yards of fabric.) Absolute value is denoted with two vertical lines or bars as $\begin{aligned} | x | \end{aligned}$ .
::绝对值是数字线上数字从零到零的距离。由于测量距离, 它总是正数或零。 (记住, 注意不要有人去商店, 要求到 - 8 英尺的木材或 - 2 码的织物。) 绝对值用两条垂直线或条表示为 x 。

lesson content

Absolute Value and the Distance Between Two Points on the Number Line
::绝对值和数字行两点之间的距离

The absolute value of a number is
::数字的绝对值是

\begin{aligned} | a | = {\begin{cases} a & if a \geq 0 \\ - a & if a < 0 \end{cases} \end{aligned}

::~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

We can use this to define the distance between two points on the number line, say b and a , as $\begin{aligned} | b - a | \end{aligned}$ .
::我们可以用这个来定义数字线上两个点之间的距离, 例如 b 和 a , 作为 b- a 。

Example 5
::例5

Find the absolute values of: 5, -2, 0, -2.07, and $\begin{aligned} π \end{aligned}$ .

::查找绝对值为: 5, 2, 0, - 2.07, 和。

Solution:
::解决方案 :

\begin{aligned} | 5 | = 5 & | - 2 | = 2 & | 0 | = 0 & | - 2.07 | = 2.07 & | π | = π \end{aligned}

WARNING
::警告

Finding the absolute value of a number does not always change the sign of the number. For example, $\begin{aligned} | 4 | \neq - 4 \end{aligned}$ .
::查找数字的绝对值并不总能改变数字的符号。例如,%4+4+4。

Example 6
::例6

Find the distance between 6 and -7 on the number line.
::在数字行中查找 6 和 - 7 之间的距离。

Solution: Use the formula above and say 6 is b and -7 is a . Then, $\begin{aligned} | 6 - (- 7) | = | 6 + 7 | = | 13 | = 13 \end{aligned}$ . 6 is 13 units from -7 on the number line and vice versa.
::解答: 使用上面的公式, 并说 6 是 b 和 - 7 是 a。然后, 6 - (- 7)\\\\\\\\\ 6+7\\\\\\\\ 13\13。 6 是 - 7 的 13 。 6 是 - 7 的 13 。在数字线上是 13 个单位, 反之亦然。

by Donna Gaudet demonstrates how to find the absolute value of real numbers.
::Donna Gaudet展示了如何找到真实数字的绝对值。

Feature: Under Pressure
::特征: 压力下

by Kathy Kehrli and Deirdre Mundy
::作者:凯西·凯尔利和德尔德勒·蒙迪

If high blood pressure is bad for your health, that means that low blood pressure should be good, right? Not exactly. There is a normal range for an adult's blood pressure. Results that are too far above or too far below the normal range can both be unhealthy. To determine whether a patient's blood pressure reading puts them at risk, doctors use absolute values.
::如果高血压对身体健康有害,这意味着低血压应该是好的,对吗?并非完全如此。成年人的血压有一个正常的范围。超过或远远低于正常范围的结果都是不健康的。为了确定病人的血压读数是否使他们处于危险之中,医生使用绝对值。

Happy Mediums
::快乐中

Blood pressure measurements yield two numbers, the systolic and diastolic pressures. The systolic pressure is the pressure on your blood vessels when your heart is pumping blood. The diastolic pressure is the pressure on your veins when your heart is resting. Doctors will give you your blood pressure reading with the systolic number on top and the diastolic number on the bottom.
::血压测量产生两个数字, 左侧和右侧压力。右侧压力是心脏抽血时对血管的压力。右侧压力是心脏休息时对血管的压力。医生会用顶部的左侧数字和底部的右侧数字向您提供血液压力读数。

The average healthy blood pressure reading for an adult is $\begin{aligned} \frac{120}{80} \end{aligned}$ mmHg. The further your blood pressure falls beyond this figure, the more likely you are to experience severe health problems. People with high blood pressure can suffer from heart failure, stroke, or kidney failure. People with low blood pressure often experience fainting, dizziness, and nausea.
::成年人的平均健康血压读数为12080毫米Hg。你的血压越低,你就越可能遇到严重的健康问题。高血压的人可能患有心脏病、中风或肾衰竭。低血压的人往往会晕倒、晕眩和恶心。

Just how high is too high and how low is too low? To determine this, doctors use the absolute value expressions $\begin{aligned} | S - 120 | \end{aligned}$ and $\begin{aligned} | D - 80 | \end{aligned}$ , where $\begin{aligned} S \end{aligned}$ is the patient's systolic pressure and $\begin{aligned} D \end{aligned}$ is the patient's diastolic pressure. If the value of either (or both) of these expressions is larger than 20, the patient might be at risk.
::高多少高,低多少?为了确定这一点,医生使用绝对值表达式 QS- 120 和 QD- 80 。 S 是病人的收缩压力, D 是病人的截取压力。如果这些表达式中任何一个(或两个)的数值都大于20, 病人可能面临风险。

If you lined up all the blood vessels in your body, they would be 60,000 miles long. Moreover, each day they carry the equivalent of over 2,000 gallons of blood to the body's tissues. What effect does this pressure have on the walls of the blood vessel? Find out in by TED-Ed.
::如果你把体内所有的血管都排成一排,它们会长60,000英里。此外,它们每天携带相当于2,000加仑血液的血液到身体的组织上。这种压力对血管的墙壁有什么影响?请在TED-Ed中查证。

Summary
::摘要

We can use $\begin{aligned} < \end{aligned}$ , $\begin{aligned} \leq \end{aligned}$ , $\begin{aligned} > \end{aligned}$ , and $\begin{aligned} \geq \end{aligned}$ to compare numbers.
::我们可以使用 < 、、、 > 和来比较数字。

To compare numbers, we can use their decimal forms and place value to compare them.
::为了比较数字,我们可以使用他们的小数表格和位置价值来比较它们。

The absolute value of a number is the distance of the number from zero on the number line.
::数字的绝对值是数字线上数字从零到零的距离。

Review
::回顾

Plot the following numbers on a number line. Use an appropriate scale.
::在数字行中绘制以下数字。使用适当的比例尺。

$\begin{aligned} - 1, 0.3, \sqrt{2} \end{aligned}$
$\begin{aligned} - \frac{1}{4}, - 2 \frac{1}{2}, 3.15 \end{aligned}$
$\begin{aligned} 1.4, \frac{5}{6}, \sqrt{9} \end{aligned}$
$\begin{aligned} - \sqrt{6}, \frac{4}{3}, π \end{aligned}$

Order the following sets of numbers from least to greatest.
::排序以下数组,从最小数到最大数组。

$\begin{aligned} - 4, - \frac{9}{2}, - \frac{1}{3}, - \frac{1}{4}, - π \end{aligned}$
$\begin{aligned} 0, - \frac{1}{2}, \frac{4}{5}, \frac{1}{6}, - \sqrt{\frac{1}{3}} \end{aligned}$

Order the following sets of numbers from greatest to least.
::顺序排列以下从最大到最小的一组数字。

$\begin{aligned} 3.68, 4 \frac{1}{2}, 5, 3 \frac{11}{12}, \sqrt{10} \end{aligned}$
$\begin{aligned} - 2, - \frac{6}{5}, - \frac{11}{4}, - \sqrt{5}, - \sqrt{3} \end{aligned}$

Compare each pair of numbers using <, >, and =.
::用 <, > 和 = 来比较每一对数字。

$\begin{aligned} - \frac{1}{4} \underline{} - \frac{3}{8} \end{aligned}$
$\begin{aligned} \sqrt{8} \underline{} 2.9 \end{aligned}$
$\begin{aligned} - 2 \frac{8}{9} \underline{} - 2.75 \end{aligned}$
$\begin{aligned} \frac{10}{15} \underline{} \frac{8}{12} \end{aligned}$
$\begin{aligned} - \sqrt{50} \underline{} - 5 \sqrt{2} \end{aligned}$
$\begin{aligned} 1 \frac{5}{6} \underline{} 1.95 \end{aligned}$

Find the following absolute values.
::查找以下绝对值。

$\begin{aligned} | 2 - (- 3) | \end{aligned}$
$\begin{aligned} | 2 + (- 3) | \end{aligned}$
$\begin{aligned} | (- 2) - (- 3) | \end{aligned}$
$\begin{aligned} | (- 2) + (- 3) | \end{aligned}$
$\begin{aligned} | (- 2) - 3 | \end{aligned}$
$\begin{aligned} | (- 2) + 3 | \end{aligned}$

Explore More
::探索更多

1. About 0.71 of the entire Earth is made up of water. That means 0.29 of the Earth is land. What fraction of the Earth is water? What fraction of the Earth is land?
::1. 整个地球约0.71由水组成,这意味着地球0.29是陆地,地球的哪一部分是水?地球的哪一部分是陆地?

2. Locate the button $\begin{aligned} e \end{aligned}$ on your scientific calculator. $\begin{aligned} e \end{aligned}$ is sometimes called Euler's number, after the mathematician Leonard Euler, and will be used in the Exponential and Logarithmic Functions chapter.
::2. 在您的科学计算器上定位按钮e。 e 有时在数学家Leonard Euler之后称为Euler的编号, 并将用于指数和对数函数章节。

Press the $\begin{aligned} e \end{aligned}$ button. What is $\begin{aligned} e \end{aligned}$ approximately equal to?
::按下 e 按钮。约等于多少 ?

What type of real number do you think $\begin{aligned} e \end{aligned}$ is?
::你认为真实数字是什么类型?

Which number is larger: $\begin{aligned} e \end{aligned}$ or $\begin{aligned} π \end{aligned}$ ?
::哪个数字更大: e 或 ?

Which number is larger: $\begin{aligned} e \end{aligned}$ or $\begin{aligned} \sqrt{7} \end{aligned}$ ?
::哪个数字更大:e或7?

3. You can approximate the value of a square root by guessing and checking. For example, $\begin{aligned} \sqrt{5} \end{aligned}$ is between 2 and 3 because 5 is between 4 and 9.
::3. 通过猜测和检查,可以估计平方根的值。例如,5介于2至3之间,因为5介于4至9之间。

Guess a value for the square root of 5, say 2.25. $\begin{aligned} (2.25)^{2} = 5.0625 \end{aligned}$ . That is too high. Let's try a smaller number, say 2.2. $\begin{aligned} (2.2)^{2} = 4.84 \end{aligned}$ . That is too low. However, we have gotten closer: $\begin{aligned} 2.2 \leq \sqrt{5} \leq 2.25 \end{aligned}$ . We know the first decimal place is a 2.
::平方根值为 5 , 例如 2.25. (2. 25) 2 = 5. 0625 。这太高。让我们试一个小数, 比如 2.2( 2. 2) 2 = 4.84 。这太低。然而, 我们越来越接近了 : 2. 2 5 . 2. 25。我们知道小数点后的第一个位数是 2 。

To determine the second decimal place, we keep choosing numbers that are closer to each other. Let's try 2.24. $\begin{aligned} (2.24)^{2} = 5.0176 \end{aligned}$ . Close, but too high. Let's try 2.23. $\begin{aligned} (2.23)^{2} = 4.9729 \end{aligned}$ . Also close, but too low. However, we now know that $\begin{aligned} 2.23 \leq \sqrt{5} \leq 2.24 \end{aligned}$ and the second decimal place is a 3.
::为了确定第二位小数位, 我们继续选择彼此相近的数字。让我们尝试 2. 24. (2. 242) = 5. 0176. 。接近但太高。让我们尝试 2. 23 (2. 23) = 4. 9729 。也接近, 但也太低。但是, 我们现在知道 2. 235& 2. 24 和小数点后第二位是 3 。

To find the third decimal place, we repeat this process again.
::要找到小数点后第三位, 我们再次重复此进程。

$\begin{aligned} (2.234)^{2} = 4.990756 \end{aligned}$

$\begin{aligned} (2.237)^{2} = 5.004169 \end{aligned}$

$\begin{aligned} (2.235)^{2} = 4.995225 \end{aligned}$

$\begin{aligned} (2.236)^{2} = 4.999696 \end{aligned}$

So, $\begin{aligned} 2.236 \leq \sqrt{5} \leq 2.237 \end{aligned}$ . The third digit is 6.
::223652237 第三位数是6

Find $\begin{aligned} \sqrt{6} \end{aligned}$ to three decimal places by guessing and checking.
::通过猜测和检查找到小数点后6到3位位数。

4. Use the information in the Feature above to determine whether the following patients are at risk. State whether their systolic pressure, diastolic pressure, or both led to your decision.
::4. 使用上述特征中的信息来确定下列病人是否处于危险之中:

Jordan, S = 97, D = 62
::约旦,S=97,D=62

Mia, S = 119, D = 84
::米娅,S=119,D=84

Sam, S = 123, D = 81
::萨姆,S=123,D=81

Janelle, S = 105, D = 78
::Janelle, S=105, D=78

5. Consider two small companies, each of which is staffed by four employees with similar qualifications and responsibilities. For Company A, the employees’ monthly salaries are $3,000, $3,100, $3,100 and $3,200. Company B pays salaries of $2,600, $3,000, $3,300 and $3,500.
::5. 将两家小公司视为小公司,每家小公司配备四名资历和职责相似的雇员,A公司月薪为3 000美元、3 100美元、3 100美元和3 200美元,B公司月薪为2 600美元、3 000美元、3 300美元和3 500美元。

Determine the mean salary for each company by first finding the sum of the monthly salaries for each company and then dividing by the number of salaries for each company. Mean is a measure of the center (or average) of a set of data.
::确定每家公司的平均工资,首先确定每家公司的月工资总和,然后除以每家公司的工资额。平均值是一组数据的中心(或平均)的尺度。

Next, determine the mean absolute deviation in employee salaries for each company. Mean absolute deviation is a measure of the spread of a set of data. To calculate the mean absolute deviation, first subtract each data value from the mean.
::其次,确定每个公司雇员工资的绝对平均值偏差。平均绝对偏差是衡量一组数据分布的尺度。要计算平均绝对偏差, 请首先从平均值中减去每个数据值。

Next, find the absolute value of each of these differences.
::接下来,找出其中每一种差异的绝对值。

Finally, calculate the mean (see above) of these absolute differences.
::最后,计算这些绝对差异的平均值(见上文)。

On average, which company pays their employees more?
::平均而言,哪个公司给雇员的薪水更高?

Which company has a smaller spread in their employees’ salaries?
::哪个公司雇员的工资利差较小?

Answers to Review and Explore More Problems
::对审查和探讨更多问题的答复

Please see the Appendix.
::请参看附录。

PLIX
::PLIX

Try these interactives that reinforce the concepts explored in this section:
::尝试这些强化本节所探讨概念的交互作用 :

章节大纲

常规

排序实际数字和绝对值

Inequality Symbols ::不平等符号

Place Value ::位值

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

WARNING ::警告

Absolute Value ::绝对值

Absolute Value and the Distance Between Two Points on the Number Line ::绝对值和数字行两点之间的距离

Example 5 ::例5

WARNING ::警告

Example 6 ::例6

Feature: Under Pressure ::特征: 压力下

Happy Mediums ::快乐中

Summary ::摘要

Review ::回顾

Explore More ::探索更多

Answers to Review and Explore More Problems ::对审查和探讨更多问题的答复

PLIX ::PLIX

Inequality Symbols
::不平等符号

Place Value
::位值

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

WARNING
::警告

Absolute Value
::绝对值

Absolute Value and the Distance Between Two Points on the Number Line
::绝对值和数字行两点之间的距离

Example 5
::例5

WARNING
::警告

Example 6
::例6

Feature: Under Pressure
::特征: 压力下

Happy Mediums
::快乐中

Summary
::摘要

Review
::回顾

Explore More
::探索更多

Answers to Review and Explore More Problems
::对审查和探讨更多问题的答复

PLIX
::PLIX