累计年数

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Assuming that none of the students from an early group leave the cafeteria before everyone goes back to class at 12:10, what is the relative frequency of girls in the cafeteria at 11:35? What about at 11:45? 11:55?
::假设在12点10分每个人都回到班级之前,没有一群早期学生离开食堂,那么11点35分女孩在食堂的相对频率是多少?11点45分是多少?11点55分呢?

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In this lesson we discuss cumulative frequencies, and by the end of the lesson, this sort of question will be no problem at all.
::在这个教训中,我们讨论累积频率,到教训结束时,这类问题将完全不成问题。

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Cumulative frequencies describe a sort of ‘running total’ of frequencies in a frequency distribution . You will find cumulative frequencies in many real-world situations, since we often need to collect data for a larger study by conducting several smaller studies.
::累积频率在一个频率分布中描述某种频率的“持续总数 ” 。 你会发现许多现实世界情况的累积频率,因为我们经常需要通过进行一些较小的研究来收集数据,以便进行更大的研究。

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To calculate a cumulative frequency , simply create a frequency distribution table , then add the frequency from the first category to that of the second category, then add that total frequency to the third category, and so on. Because cumulative distributions don’t generally show different combinations of categories, it is a good idea to arrange your categories in a suitable order so that the cumulative frequencies are most likely to be of use as the running total increases.
::计算累积频率,简单创建一个频率分布表,然后将第一类的频率增加至第二类的频率,然后将总频率增加至第三类,等等。 由于累积分布通常不显示不同类别的组合,因此按适当顺序排列您的类别是一个好主意,这样累积频率最有可能随着总增长而使用。

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A relative cumulative frequency table shows how the cumulative frequency after each successive interval compares to the total frequency. To create a relative cumulative frequency table, calculate the relative frequency of each interval or category, and then add the relative frequency of each category to all the prior ones.
::相对累计频率表显示每个连续间隔后的累计频率与总频率的比较。要创建相对累计频率表,请计算每个间隔或类别的相对频率,然后将每个类别的相对频率添加到所有先前的间隔或类别中。

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Creating a Cumulative Frequency Table 
::创建累计频率表

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Create a cumulative frequency table showing the number of hours per week that Brian watches television, based on the given information.
::创建累计频率表, 显示Brian根据给定信息每周看电视的小时数 。

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Brian’s T.V. Time
::布赖恩的T.V.时间

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• Monday: 1.5 hrs
  ::星期一:1.5小时
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• Tuesday: 2.25 hrs
  ::星期二:2.25时
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• Wednesday: 2 hrs
  ::星期三:2时
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• Thursday: 1.75 hrs
  ::星期四:1时75分
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• Friday: 1.5 hrs
  ::星期五:1.5小时
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• Saturday: 3.25 hrs
  ::星期六: 3.25时
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• Sunday: 2.5 hrs
  ::星期日: 2.5小时

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To find the cumulative frequency of hours of T.V. watched, add the frequency of each day to the total frequency of the day before:
::要找到观看的T.V.小时的累计频率,将每天的频率增加到前一天的总频率:

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A car dealer is calculating the total sales for the past month, and wants to identify the percentage of monthly sales that have occurred after weeks 1, 2, 3, and 4. Create a relative cumulative frequency table to show the information the dealer wants.
::汽车经销商正在计算过去一个月的销售总额,并想确定第1、2、3、4周之后每月销售的百分比。 创建一个相对累积的频率表,显示经销商想要的信息。

Week Number	Cars Sold
1	21
2	12
3	17
4	24

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First total up the sales for the entire month:
::整个月销售量的首期总和如下:

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$\begin{align*}21+12+17+24=74 \ cars\end{align*}$
::21+12+17+24=74车

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Then find the relative frequencies for each week by dividing the number of cars sold that week by the total:
::然后通过将该周售出的汽车数量除以总数,找到每周的相对频率:

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• The relative frequency for the first week is:  $\begin{align*}\frac{21}{74} = .284\end{align*}$
  ::第一周的相对频率为:2174=284
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• The relative frequency for the second week is: $\begin{align*}\frac{12}{74} = .162\end{align*}$
  ::第二周的相对频率是:1274=.162。
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• The relative frequency for the third week is: $\begin{align*}\frac{17}{74} = .23\end{align*}$
  ::第三周的相对频率是:1774=23。
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• The relative frequency for the fourth week is:  $\begin{align*}\frac{24}{74} = .324\end{align*}$
  ::第四周的相对频率为:2474=324

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To find the relative cumulative frequencies, start with the frequency for week 1 and for each successive week, total all of the previous frequencies:
::要找到相对累积频率,首先从第1周的频率开始,然后连续一周的频率,所有以前的频率总数如下:

Week Number	Cars Sold	Relative Frequency	Cumulative Frequency
1	21	.284	$\begin{align*}.284\end{align*}$
2	12	.162	$\begin{align*}.284 + .162 = .446\end{align*}$
3	17	.23	$\begin{align*}.446 + .23 = .676\end{align*}$
4	24	.324	$\begin{align*}.676 + .324 = 1.0\end{align*}$

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Note that the first relative cumulative frequency is always the same as the first relative frequency, and the last relative cumulative frequency is always equal to 1.
::请注意,第一个相对累计频率总是与第一个相对频率相同,最后一个相对累计频率总是等于1。

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Constructing Tables 
::构造表格

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Create a cumulative and relative cumulative frequency table for the following data:
::为下列数据创建累计和相对累计频率表:

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Number of customers in store on Black Friday each year for the years 1995 – 2005:
::1995-2005年每年黑星期五的顾客数量:

47, 49, 48, 54, 57, 52, 61, 65, 67, 66, 70

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Label a table with the years 1995 - 2005 across the top and frequency, cumulative frequency, and relative cumulative frequency down the side. Leave 3 blanks underneath each year, and input the frequency for each year:
::标出1995- 2005年的表格,横跨表层和频度、累计频率和相对累计频率。 每年下方有3个空位,并输入每年的频率 :

Year:	1995	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005
Frequency	47	49	48	54	57	52	61	65	67	66	70
播放段落 Cumulative ::累计累计累计 播放段落 Frequency ::频率频率频率
播放段落 Relative ::相对相对相对相对 播放段落 Cumulative ::累计累计累计 播放段落 Frequency ::频率频率频率

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To calculate the cumulative frequencies, sum the total of all previous frequencies under the frequency for each year:
::为计算累计频率,在每年频率下将以往所有频率的总数相加:

Year	1995	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005
Frequency	47	49	48	54	57	52	61	65	67	66	70
播放段落 Cumulative ::累计累计累计 播放段落 Frequency ::频率频率频率	47	96	144	198	255	307	368	433	500	566	636
播放段落 Relative ::相对相对相对相对 播放段落 Cumulative ::累计累计累计 播放段落 Frequency ::频率频率频率

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To calculate the relative cumulative frequencies, divide the cumulative frequency for each year by the total cumulative frequency (636 customers, the same as the value for the last year, 2005).
::为计算相对累计频率,将每年的累计频率除以总累计频率(636名客户,与上一年(2005年)的数值相同)。

Year	1995	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005
Frequency	47	49	48	54	57	52	61	65	67	66	70
播放段落 Cumulative ::累计累计累计 播放段落 Frequency ::频率频率频率	47	96	144	198	255	307	368	433	500	566	636
播放段落 Relative ::相对相对相对相对 播放段落 Cumulative ::累计累计累计 播放段落 Frequency ::频率频率频率	.074	.151	.226	.311	.401	.483	.579	.681	.786	.890	1.0

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Earlier  Problem Revisited
::重审先前的问题

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A school lunch break is divided into multiple sessions, the 1 ^st group, consisting of 20 girls and 50 boys, begins lunch at 11:30 am, the 2 ^nd group, with 35 girls and 30 boys begins at 11:40, and the 3 ^rd group, 40 girls and 25 boys, at 11:50.
::学校午餐休息分为多个课次,第一组由20名女孩和50名男孩组成,上午11时30分开始午餐,第二组由35名女孩和30名男孩组成,上午11时40分开始,第三组由40名女孩和25名男孩组成,上午11时50分开始午餐。

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Assuming that none of the students from an early group leave the cafeteria before everyone goes back to class at 12:10, what is the relative frequency of girls in the cafeteria at 11:35? What about at 11:45? 11:55?
::假设在12点10分每个人都回到班级之前,没有一群早期学生离开食堂,那么11点35分女孩在食堂的相对频率是多少?11点45分是多少?11点55分呢?

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First create a table showing each session and the number of boys and girls in each session:
::首先建立一张表格,列出每届会议和每届会议的男女生人数:

Session 1 - 11:30		Session 2 - 11:40		Session 3 - 11:50
Boys	Girls	Boys	Girls	Boys	Girls
50	20	30	35	25	40

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Next, add a row to the bottom of your table for cumulative relative frequency of girls:
::下一个,在表格下方添加一行,说明女孩累计相对频率:

Session 1		Session 2		Session 3
Boys	Girls	Boys	Girls	Boys	Girls
50	20	30	35	25	40
Girls: $\begin{align*}\frac{20}{70}=.286\end{align*}$  or 28.6 %		Girls: $\begin{align*}\frac{55}{135}=.407\end{align*}$  or 40.7%		Girls: $\begin{align*}\frac{95}{200}=.475\end{align*}$  or 47.5%

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Examples 
::实例

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For 25 days, the snow depth at Whiteout Mountain was measured (to the nearest inch) and recorded as follows:
::在25天的时间里,对怀特特特山的雪深进行了测量(至最近的英寸),记录如下:

242, 228, 217, 253, 239, 266, 242, 251, 240, 223, 219, 246, 260, 258, 225, 234, 230, 249, 245, 254, 243, 235, 231, 257

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1. Determine a reasonable class interval
   ::确定合理的类别间隔
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2. Set up a frequency distribution table
   ::设置频率分布表
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3. Find the frequency for each class interval
   ::查找每个类间隔的频率
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4. Calculate the cumulative frequencies progressively from left to right
   ::从左向右逐步计算累积频率
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5. Use the information gathered from the frequency distribution table to plot a cumulative frequency graph.
   ::使用从频率分布表收集的信息绘制累计频率图。

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Solutions:
::解决办法:

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Example 1
::例1

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Determine a reasonable class interval
::确定合理的类别间隔

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The values range 217 – 266, a class interval of 10 would break the data up into a reasonable 6 bins .
::值范围为 217 - 266, 类别间距为 10 , 将数据折成合理的 6 个文件夹 。

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Example 2
::例2

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Set up a frequency distribution table, and find the frequency for each class interval
::设置频率分布表, 并查找每个类间隔的频率

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Create a table with the intervals noted across the top, and the frequency of each below: 
::创建一个表格,表格应显示上方的间隔,并显示以下各位的频率:

210-220	220-230	230-240	240-250	250-260	260-270
2	3	5	7	5	2

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Example 3
::例3

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Add another row and calculate the cumulative frequency.
::添加另一行并计算累积频率。

Interval:	210-220	220-230	230-240	240-250	250-260	260-270
Frequency:	2	3	5	7	5	2
Cumulative Frequency:	$\begin{align*}\frac{2}{24} \ 8.33\%\end{align*}$	$\begin{align*}\frac{5}{24} \ 20.83\%\end{align*}$	$\begin{align*}\frac{10}{24} \ 41.66\%\end{align*}$	$\begin{align*}\frac{17}{24} \ 70.83\%\end{align*}$	$\begin{align*}\frac{22}{24} \ 91.66\%\end{align*}$	$\begin{align*}\frac{24}{24} \ 100\%\end{align*}$

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Review 
::回顾

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1. A weather forecaster highlights the lows over-night for the past 30 days in a small town in Wisconsin. The temperature readings are given in Fahrenheit, and are shown below. Use the data to complete the frequency table.
::1. 天气预报员着重介绍威斯康星一个小城镇过去30天的夜间低温,温度读数以法赫伦海特为单位,如下文所示:利用数据完成频率表。

$$\begin{align*}&41^\circ, 58^\circ, 61^\circ, 54^\circ, 49^\circ, 46^\circ, 52^\circ, 58^\circ, 67^\circ, 43^\circ, 47^\circ, 60^\circ, 52^\circ, 58^\circ, 48^\circ,\\ & 44^\circ, 59^\circ, 66^\circ, 62^\circ, 55^\circ 44^\circ, 49^\circ, 62^\circ, 61^\circ, 59^\circ, 54^\circ, 57^\circ, 58^\circ, 63^\circ, 60^\circ\end{align*}$$

Interval	Tally	Frequency
40 - 44
45- 49
50 - 54
55 - 59
60 - 64
65 - 69

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2. The following represents scores that a class received on their most recent Biology test. Complete the frequency table below.
::2. 以下为某一类最近进行生物学测试后获得的分数,填写以下频率表。

58, 79, 81, 99, 68, 92, 76, 84, 53, 57, 81, 91, 77, 50, 65, 57, 51, 72, 84, 89

Interval	Tally	Frequency
50 - 59
60 - 69
70 - 79
80 - 89
90 - 99

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3. James received the following scores on his quizzes in US History over the course of 1 year. Complete the frequency table below using the scores:
::3. James在一年中在美国历史的测验中获得以下分数。

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85, 72, 97, 81, 77, 93, 100, 75, 86, 70, 96, and 80.
::85、72、97、81、77、93、100、75、86、70、96和80。

Interval/Grades	Tally	Frequency
61 - 70
71 - 80
81 - 90
91 - 100

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4. Sue competed against 14 others in a time trial for the 400-meter run at the state finals. Their times have been recorded in the table below. What percent of the runners completed the time trial between 50 and 53.9 seconds?
::4. Sue在州决赛400米赛跑的时试中与其他14人竞争,其时间记录在下表。 50至53.9秒之间,有多少跑者完成了时试?

400 Meter Run Time Trails

Interval	Tally	Frequency
50.0 - 50.9		0
51.0 - 51.9	$\begin{align*}||\end{align*}$	2
52.0 - 52.9	$\begin{align*}\cancel{|||| \ |}\end{align*}$	6
53.0 - 53.9	$\begin{align*}|||\end{align*}$	3
54.0 - 54.9	$\begin{align*}||||\end{align*}$	4

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5. The following data is the starting weights of 30 adults, in pounds, who participated in a study on weight loss. Use the data to create a cumulative frequency table. Determine appropriate intervals for the weights given.
::5. 下列数据是30名成年人(磅)的起始重量,他们参加了关于体重减重的研究,利用这些数据编制累计频率表,确定加权的适当间隔。

195, 206, 100, 98, 150, 210, 195, 106, 195, 168, 180, 212, 104, 195, 100, 216, 195, 209, 112, 99, 206, 116, 195, 100, 142, 100, 135, 98, 160, 155

Weight of Adults before diet program participation

Interval	Frequency	Cumulative Frequency

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6. The following table shows the weights in pounds for students attending a “Get Fit” summer program. Use the data to find cumulative frequency.
::6. 下表显示了参加 " 健身 " 暑期方案的学生的体重(磅),利用数据来寻找累积频率。

Weights of “Get Fit” camp students

Interval	Frequency	Cumulative Frequency
91-100	6
101-110	3
111-120	0
121-130	3
131-140	0
141-150	2
151-160	2

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7. 20 students were asked how many meals their family eats out in one week. The results are listed below. Complete the frequency table using this data.
::7. 20名学生被问及一周内有多少家庭用餐,结果如下:

{6, 5, 4, 5, 0, 7, 1, 5, 4, 4, 3, 2, 2, 3, 2, 4, 3, 4, 0, 7}

Number of Meals Out

Interval	Tally	Frequency	Cumulative Frequency
0-1
2-3
4-5
6-7

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8. The following graph shows the participants in Jane’s aerobics classes. How many total students does she teach on the given day?
::8. 下图显示了Jane有氧运动班的参加者,她当天教多少学生?

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9. The following table shows a cumulative frequency distribution of the ages of tri-athletes. According to the table, how many tri-athletes are in their forties?
::9. 下表显示了三个民族组年龄的累计频率分布:根据该表,40多岁的三民族组有多少个?

Cumulative Frequency Distribution of Tri-Athlete Ages

Age Group	Total
20 - 29	8
20 - 39	18
20 - 49	25
20 - 59	31
20 - 69	35

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10. The quiz scores for a job placement math assessment for the 10 applicants were: 61, 67, 81, 83, 87, 88, 89, 90, 98, and 100. Which frequency table is accurate for this set of data?
::10. 对10名申请人进行职位安排数学评估的测验分数是:61、67、81、83、87、88、89、90、98和100。 这一组数据哪个频率表准确?

Interval	Freq	Interval	Freq	Interval	Freq	Interval	Freq
61 - 70	2	61 - 70	2	61 - 70	2	61 - 70	2
71 - 80	0	71 - 80	2	71 - 80	0	71 - 80	2
81 - 90	8	81 - 90	8	81 - 90	6	81 - 90	7
91 - 100	10	91 - 100	10	91 - 100	2	91 - 100	10

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It is that time of year again. It is Easter, and it is time to hunt eggs. The kids have been divided up into age groups, and their eggs hidden in different areas of a large park. The adult leaders have gathered the data from the three age groups: “Kinders”, “Pee Wee”, and “Big Eggs”, and compiled the results into frequency tables. The problem is, each of the adult leaders reported their information differently.
::现在又是复活节,现在是打鸡蛋的时候了。孩子们被分成年龄组,他们的鸡蛋隐藏在一个大公园的不同区域。成年领导人从三个年龄组“Kinders”、“Pee Wee”和“Big Eggs”收集了数据,并将结果汇编成频率表。问题在于,每个成年领导人报告的情况不同。

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For questions 11-13, use the data gathered by each adult leader and follow the instructions for interpreting the data given by each.
::对于问题11-13,使用每个成年领导人收集的数据,并遵循解释每个成人领导人提供的数据的指示。

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11. Team “Kinders” coach reported the following results for the number of eggs found by the kiddos in their group, convert them to a cumulative frequency chart.
::11. " Kinders " 队教练报告了他们组中孩子发现的蛋数的以下结果,将其转换成累计频率图。

Time (s) in minutes	Frequency of Eggs Found
0 - 5	20
5 - 10	35
10 - 15	15
15 - 20	22
20 - 25	8
25 - 30	9

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12. Team “Pee Wee” also did a great job of finding eggs. Their results were recorded in a cumulative frequency table, convert to a frequency table.
::12. " Pee Wee " 小组在寻找鸡蛋方面也做了出色的工作,其结果记录在累计频率表中,转换成频率表。

Time (s) in minutes	Cumulative Frequency of Eggs Found
0 - 5	20
5 - 10	27
10 - 15	31
15 - 20	31
20 - 25	37
25 - 30	50

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13. The “Big Eggs” were the champions the last three years running. They are known for always collecting the same amount of eggs in each interval. This year they collected a total of 120 eggs.
::13. " 大鸡蛋 " 是过去三年的冠军,众所周知,它们每间隔收集的鸡蛋数量始终相同,今年共收集120个鸡蛋。

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1. Complete a frequency chart
   ::完成频率图表
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2. Complete a cumulative frequency chart
   ::完成累计频率图表

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Review (Answers)
::回顾(答复)

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Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。