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  [Figure 1]

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  Sara's cat has a new litter of kittens each year. She has been keeping track of how many kittens are in each litter. Sara wants to know what the typical amount of kittens is in each litter. To do this, she could find the middle amount of kittens that have been born. Here is Sara's  data . Each number represents an amount of kittens that were born in one year.
  ::Sara的猫每年都有一群新的小猫。 她一直在追踪每只小猫中有多少只小猫。 Sara想知道每只小猫中通常有多少小猫。 为此, 她可以找到中产小猫。 这是Sara的数据。 每个数字代表了一年中出生的小猫的数量 。

  7, 8, 9, 12, 14, 10, 15, 14

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  How can Sara find that middle number in her  data set ?
  ::Sara如何在数据组中找到中间数字?

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  In this concept, you will learn how to find the median of a set of data.
  ::在这个概念中,你会学会如何找到一组数据的中位数。

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  Median
  ::中中

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  The  median  of a set of data is the middle score or number of the data. Median can be useful in examples like finding the median amount of money or median time a runner takes to run a race.
  ::一组数据的中位数是中间分数或数据数。 中位数在诸如找到中位数货币或中位数跑步者赛跑时的中位数等例子中可能是有用的。

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  Here is a set of data. To find the median there are a few steps.
  ::以下是一组数据。要找到中位数,有几步。

  2, 5, 6, 2, 8, 11, 13, 14, 15, 21, 22, 25, 27

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  First, write the numbers in order from the least to greatest. Be sure to include repeated numbers in the list.
  ::首先, 写入从最小到最大的数字。 请务必在列表中包含重复数字 。

  2, 2, 5, 6, 8, 11, 13, 14, 15, 21, 22, 25, 27

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  Next, find the middle number of the set of data.
  ::下一步,找到数据集的中间数字。

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  In this set, there is an odd number of values in the set. There are thirteen numbers in the set. Count 6 on one side of the median and 6 on the other side of the median.
  ::在此集中, 在集中有奇数的值。 集中有13个数。 中位数的一边计数 6 , 中位数的另一边计数 6 。

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  The answer is 13.
  ::答案是13岁

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  This set of data was easy to work with because there was an odd number of values in the set. It does not always work out that way, though. Sometimes, there is an even number of items in the data set.
  ::这组数据很容易使用,因为集中有奇数的值,但并不总是这样算出。有时数据集中有偶数的项目。

  4, 5, 12, 14, 16, 18

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  Here, there are six values in the data set. They are already written in order from least to greatest. This data set has two values in the middle because there are six values.
  ::这里, 数据集中有 6 个值。 它们已经按照从最小到最大顺序写入 。 此数据集中间有两个值, 因为有 6 个值 。

  4, 5,  12, 14,  16, 18

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  The two middle values are 12 and 14. To find the median, add the two middle values together and divide by 2. This is basically taking an  average  of the two middle values.
  ::两个中间值是12和14。 要找到中位数, 将两个中间值加在一起, 并除以2。 这基本上需要两个中间值的平均值。

  $$\begin{array}{rl}12+14& =26\\ 26÷2& =13\end{array}$$

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  The median score is 13.
  ::中位分是13分。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Sara and her kittens.
  ::早些时候,你得到一个问题 关于莎拉和她的小猫咪。

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  She wants to find the middle value of a data set, which is known as finding the median. Here is Sara's data that shows how many kittens were born in each litter:
  ::她想要找到一个数据集的中间值, 即找到中位数。 这是Sara的数据, 显示每个垃圾中有多少只小猫出生:

  7, 8, 9, 12, 14, 10, 15, 14

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  First, Sara needs to put her data in order from least to greatest.
  ::首先,Sara需要把她的数据从最低到最高排列

  7, 8, 9, 10, 12, 14, 14, 15

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  Next, Sara needs to count the number of items in her data set in order to continue on following the correct steps. There are 8 values in her data set, an even number.
  ::接下来,Sara需要计算其数据集中的项目数量, 以便继续遵循正确的步骤。 她的数据集中有8个值, 一个偶数 。

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  Then, Sara has to find the two middle values, since there is an even number, and then find the average of those two middle values.
  ::然后,Sara必须找到两个中间值, 因为有一个偶数, 然后找到这两个中间值的平均值。

  $$\begin{array}{rl}10+12& =22\\ 22÷2& =11\end{array}$$

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  The answer is 11. The median number of kittens born each year is 11 per litter.
  ::答案是11. 每年出生的猫的中位数是每只小猫11只。

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  Example 2
  ::例2

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  Jess has planted a garden. His big crop has been eggplant. Jess harvested the following numbers of eggplant over five days. What is the median number of eggplant harvested?
  ::杰西种植了一个花园,他的大作物是茄子。杰西在五天内收获了以下数量的茄子。茄子的中位数是多少?

  12, 9, 15, 6, 9

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  First, write the numbers in order from least to greatest.
  ::首先,写下数字,从最少到最大的顺序。

  6, 9, 9, 12, 15

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  Next, count two numbers on each side of the middle of the data set to narrow down to the median number.
  ::接下来,在数据组中间的每个侧边数两个数字,以缩小到中位数。

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  Then, find the middle score.
  ::然后找到中间分数

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  The answer is 9 eggplants in the median number harvested.
  ::答案是中位数的9种茄子。

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  Example 3
  ::例3

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  Find the median of the following data set.
  ::查找以下数据集的中位数。

  11, 5, 8, 6, 15

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  First, order the numbers from least to greatest.
  ::首先,将数字从最小到最大顺序排列。

  5, 6, 8, 11, 15

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  Next, count the total number of items in the data set to determine how many to count in from each side.
  ::下一步,计算数据集中的项目总数,以确定每一侧有多少项要计算。

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  Then, count in until the median is reached.
  ::然后,计数到中位数到达。

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  The answer is 8.
  ::答案是8岁

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  Example 4
  ::例4

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  Find the median of the following data set.
  ::查找以下数据集的中位数。

  4, 1, 6, 9, 2, 11

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  First, order the numbers from least to greatest.
  ::首先,将数字从最小到最大顺序排列。

  1, 2, 4, 6, 9, 11

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  Next, count the total number of items in the data set to determine how many to count in. In this case, there are 6 numbers in the data set, which means an even number of items. 
  ::接下来,计算数据集中的项目总数,以确定要计算的项目数量。 在这种情况下,数据集中有6个数字,这意味着偶数的项目数量。

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  Then, since there are an even number of values in the data set, an average needs to be taken of the two middle values.
  ::然后,由于数据集中的数值是偶数,因此需要采用两个中间值的平均值。

  $$\begin{array}{rl}4+6& =10\\ 10÷2& =5\end{array}$$

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  The answer is 5.
  ::答案是5。

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  Example 5
  ::例5

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  Find the median of the following data set.
  ::查找以下数据集的中位数。

  63, 23, 78, 34, 56, 89

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  First, order the numbers from least to greatest.
  ::首先,将数字从最小到最大顺序排列。

  23, 34, 56, 63, 78, 89

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  Next, count the total number of items in the data set. There is an even number of items in the data set.
  ::下一步,在数据集中计数项目总数。数据集中有偶数的项目。

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  Then, since there are 6 values in the set, take an average of the middle two values to determine the median.
  ::然后,由于集中有6个值,用中间两个值的平均值来确定中位数。

  $$\begin{array}{rl}56+63& =119\\ 119÷2& =59.5\end{array}$$

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  The answer is 59.5
  ::答案是59.5

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  Review
  ::回顾

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  Find the median for each pair of numbers.
  ::找到每一对数字的中位数。

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  1. 16 and 19
     ::16和19
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  2. 4 and 5
     ::第四条和第五条
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  3. 22 and 29
     ::第22和29段
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  4. 27 and 32
     ::27和32
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  5. 18 and 24
     ::18和24

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  Find the median for each set of numbers.
  ::查找每组数字的中位数。

  6. 4, 5, 4, 5, 3, 3
  7. 6, 7, 8, 3, 2, 4
  8. 11, 10, 9, 13, 14, 16
  9. 21, 23, 25, 22, 22, 27
  10. 27, 29, 29, 32, 30, 32, 31
  11. 34, 35, 34, 37, 38, 39, 39
  12. 43, 44, 43, 46, 39, 50
  13. 122, 100, 134, 156, 144, 110
  14. 224, 222, 220, 222, 224, 224
  15. 540, 542, 544, 550, 548, 547