Section outline


  • lesson content

    Bob the weatherman records the high temperature each day for two weeks in June. He wants to see how much the temperature changes throughout those two weeks. Here is the  data  he collected for the 14 days he was keeping track of temperature highs:
    ::天气预报员鲍勃在六月每天记录高温两周。 他想看看这两周的温度变化。 这是他收集的14天的数据, 记录温度高:

    72, 75, 68, 70, 67, 76, 71, 72, 68, 75, 71, 75, 69, 70

    In order for Bob to know the difference in high temperatures throughout the two weeks, he needs to find the  range  of the data.
    ::为了让鲍勃知道这两周的高温差异 他需要找到数据的范围

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

    Range
    ::范围范围范围

    The  range  of a set of data simply tells where the numbers fall and whether data in set is close together or spread apart. A set of data with a small range tells us something different than a set of data with a large range. 
    ::一组数据的范围简单说明数字的下降地点,以及数据集中的数据是相近的还是分散的。 一组小范围的数据集告诉我们不同于一组大范围的数据集。

    To find the range of a set of data:
    ::要找到一组数据的范围:

    1. Put the values in the  data set  in numerical order. This will show which is the greatest number in the set (the maximum), and which is the smallest number (the minimum).
      ::将数值按数字顺序排列数据集中的值。这将显示数据集中哪个数字最多(最大),哪个数字最小(最低)。
    2. Subtract the  minimum  from the  maximum . This is the range of the data.
      ::从最大值中减去最小值。这是数据的范围。

    Take a look at the data set below.
    ::看一下下面的数据集。

    11, 9, 8, 12, 11, 11, 14, 8, 10

    First, arrange the data in numerical order.
    ::首先,按数字顺序排列数据。

    8, 8, 9, 10, 11, 11, 11, 12, 14

    Next, identify the minimum and maximum of the set. The minimum is 8 and the maximum is 14.
    ::下一步,确定设定的最小值和最大值。最低值为8,最高值为14。

    Then, subtract the minimum from the maximum to find the range.
    ::然后从最大值中减去最小值,以找到范围。

    14 − 8 = 6

    The range of the data set is 6. This means that all of the numbers in the data set fall within six places of each other. All of the data results are fairly close together.
    ::数据集的范围是6,这意味着数据集中的所有数字都位于6个位置内,所有数据结果都相当接近。

    The context of a set of data and its range can reveal important information about the data. For example, if a data set showing plant growth using special soil is 4, that shows that the plants all grew in close range to each others. In other words, the special soil had the same impact on all of the plants. Suppose though, the data showed a wider range of 15. That would signify that perhaps the special soil did not have as equal of an impact on the plants as some grew a lot and some grew little to make that range so wide.
    ::一组数据的背景及其范围可以揭示有关数据的重要信息。 例如,如果一组显示使用特殊土壤的植物生长的数据集是4, 显示植物生长的距离很近。 换句话说, 特殊土壤对所有植物都具有同样的影响。 假设数据显示范围更广的有15个。 这表示特殊土壤对植物的影响可能不如某些植物长得那么大,而有些则没有长得那么大。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Bob and his weather  statistics .
    ::早些时候,你得到一个问题 关于鲍勃和他的天气统计。

    Bob kept track of the high temperatures for two weeks to see the difference in temperature. Here was is data:
    ::Bob在两周内跟踪高温, 以观察温度的差异。这里的数据是:

    72, 75, 68, 70, 67, 76, 71, 72, 68, 75, 71, 75, 69, 70

    Bob needs to find the range of his data to determine the range in temperature from these two weeks.
    ::Bob需要找到数据范围 以确定这两周的温度范围

    First, Bob puts the data in numerical order.
    ::首先,鲍勃将数据按数字顺序排列。

    67, 68, 68, 69, 70, 70, 71, 71, 72, 72, 75, 75, 75, 76

    Next, Bob identifies the minimum and maximum of the data set. The minimum is 67 and the maximum is 76. These data points mean that both were the high temperatures one day in those two weeks, but the weather clearly changed course at some point.
    ::其次, Bob 指出数据集的最小值和最大值。最小值为67,最大值为76。这些数据点意味着这两个星期的一天温度都是高的,但天气在某个时候显然改变了方向。

    Then, Bob subtracts the minimum from the maximum.
    ::然后,鲍勃从最大值中减去最低值。

    76 − 67 = 9
     

    The answer is 9. There was a 9 degree change in temperature at some point throughout the two weeks that Bob kept track of high temperatures.
    ::答案是9. 鲍伯在这两周里 在某个时间点 温度发生了9度的变化 鲍伯一直跟踪高温

    Example 2
    ::例2

    The following is the number of patrons at a local movie theater. What is the range of the data?
    ::以下是当地电影院的赞助者人数。数据的范围是多少?

    26, 22, 40, 45, 46, 18, 30, 80, 60, 75

    To figure this out, we need to find the difference between the highest number of patrons and the lowest number of patrons.
    ::为了弄清这一点,我们需要找出赞助者人数最多和赞助者人数最少之间的差别。

    First, put the data in order from least to greatest.
    ::首先,把数据从最小到最大排列顺序。

    18, 22, 26, 30, 40, 45, 46, 60, 75, 80

    Next, identify the minimum and maximum of the data set. The minimum is 18 and the maximum is 80.
    ::其次,确定数据集的最低值和最高值,最低值为18,最高值为80。

    Then, subtract the minimum from the maximum to find the range.
    ::然后从最大值中减去最小值,以找到范围。

    80 − 18 = 62

    The answer is 62. This shows there is a wide range of people who attend the movies in that data set. There is not consistent attendance at the movies. 
    ::答案是62,这显示在数据集里有各种各样的人看电影,没有连续看电影。

    Example 3
    ::例3

    Find the range of the following data set.
    ::查找以下数据集的范围。

    4, 5, 6, 9, 12, 19, 20

    First, put the numbers in numerical order. This data set is already in order.
    ::首先,按数字顺序排列数字。这个数据集已经排列好了。

    Next, identify the minimum and maximum of the data set. The minimum is 4 and the maximum is 20
    ::下一步,确定数据集的最小值和最大值。最小值为 4, 最大值为 20

    Then, subtract the minimum from the maximum to find the range.
    ::然后从最大值中减去最小值,以找到范围。

    20 − 4 = 16

    The answer is 16.
    ::答案是16岁

    Example 4
    ::例4

    Find the range of the following data set.
    ::查找以下数据集的范围。

    5, 2, 1, 6, 8, 20, 25

    First, put the numbers in numerical order.
    ::首先,按数字顺序排列数字。

    1, 2, 5, 6, 8, 20, 25

    Next, identify the minimum and maximum of the data set. The minimum is 1 and the maximum is 25.
    ::下一步,确定数据集的最低值和最高值,最低值为1,最高值为25。

    Then, subtract the minimum from the maximum to find the range.
    ::然后从最大值中减去最小值,以找到范围。

    25 − 1 = 24

    The answer is 24.
    ::答案是24个。

    Example 5
    ::例5

    Find the range of the following data set.
    ::查找以下数据集的范围。

    65, 23, 22, 45, 11, 88, 99, 123, 125

    First, put the numbers in numerical order.
    ::首先,按数字顺序排列数字。

    11, 22, 23, 45, 65, 88, 99, 123, 125

    Next, identify the minimum and maximum of the data set. The minimum is 11 and the maximum is 125.
    ::下一步,确定数据集的最低值和最高值,最低值为11,最高值为125。

    Then, subtract the minimum from the maximum to find the range.
    ::然后从最大值中减去最小值,以找到范围。

    125 − 11 = 114

    The answer is 114.
    ::答案是114。

    Review
    ::回顾

    Find the range for each set of data.
    ::查找每组数据的范围。

    1. 4, 5, 4, 5, 3, 3
    2. 6, 7, 8, 3, 2, 4
    3. 11, 10, 9, 13, 14, 16
    4. 21, 23, 25, 22, 22, 27
    5. 27, 29, 29, 32, 30, 32, 31
    6. 34, 35, 34, 37, 38, 39, 39
    7. 43, 44, 43, 46, 39, 50
    8. 122, 100, 134, 156, 144, 110
    9. 224, 222, 220, 222, 224, 224
    10. 540, 542, 544, 550, 548, 547
    11. 2, 3, 3, 3, 2, 2, 2, 5, 6, 7
    12. 4, 5, 6, 6, 6, 7, 3, 2
    13. 23, 22, 22, 24, 25, 25, 25
    14. 123, 120, 121, 120, 121, 125, 121
    15. 678, 600, 655, 655, 600, 678, 600, 600