Further Mathematics TOPIC1 univariate data 教学课件 全集.ppt

1、Further Mathematics TOPIC 1 Univarate data 单变量数据,进阶数学,1.学习计划： 11月23日-1月10日 Topic1-4 2月6日-4月10日 Topic 5-9 5月1日-11月1日 Topic10 高考复习 2. 学习材料： 纸质课本和电子课本相结合（QQ群） 说明书与实际操作相结合（CAS计算器） 历年试卷和模拟试卷相结合（过去十年) .au/ .au/Pages/vce/studies/mathematics/further/exams.aspx,几点重

2、要说明,3.学习方向： 平时的认真为SAC（ 三分之一） 复习时的拼搏为EXAM( 三分之二） 最终为了有更好的ATAR,更多的选择机会 4.学习工具 用好书本 用好计算器 用好书上的笔记 用好书上的单词，概念，例题，练习,几点重要说明,5.学习要求： 看书：（再忙也得阅读书本：可以课前，可以作业前） 单词：随时记录和查阅，翻译 计算器：掌握每一个功能的操作技巧 笔记：最好记在书本上，因为两个EXAM 都可以带书本 作业：及时上交，真诚书写,几点重要说明,本书 大致 概况,Further Mathematics 进阶数学,TOPIC 1,Univariate Data,1.1 kick off

3、 with CAS,Types of data Univariate data(单变量数据） are data that contain one variable. That is, the information deals with only one quantity that changes. Therefore, the number of cars sold by a car salesman during one week is an example of univariate data.,univariatejunvertadj. 数 单变量的,datadetn. 数据；资料,v

4、ariableverb()ladj. 变量的；可变的；易变的，多变的；变异的，生物 畸变的 n. 数 变量；可变物，可变因素,Types of data Sets of data that contain two variables are called bivariate data（双变量数据） and those that contain more than two variables are called multivariate data（多变量数据）. Data can be classified as either numerical（数值的） or categorical（分类的

5、）. The methods we use to display data depend on the type of information we are dealing with.,bivariatebavrit adj. 二变量的,numericalnjumerk()ladj. 数值的；数字的；用数字表示的（等于numeric）,categoricalktgrk()l adj. 绝对的；直接了当的；无条件的；属于某一范畴的，分类的，按类别的，,containkntenv.包含；含有；控制；容纳；包括；遏制；包容,multivariatemltvert多变量；多元；,Types of da

6、ta Numerical data （数值数据）is data that has been assigned a numeric value. Numerical data can be: discrete(离散的） data that can be counted but that can have only a particular value, for example the number of pieces of fruit in a bowl可以计数但仅具有某个特定值的数据，例如碗中的水果的数量 continuous（连续的） data that is not restricted

7、to any particular value, for example the temperature outside, which is measured on a continuous scale.数据，其不限于任何特定值，例如：以连续尺度测量的外部温度,1.discretedskritadj. 离散的，不连续的 n. 分立元件；独立部件,2.continuouskntnjsadj. 连续的，持续的；继续的；连绵不断的,particular value ptikjul vlju特值；,restricted rstrktdadj有受限制的；保密的；v.限制( restrict的过去式),W

8、hich of the following is not numerical data? A Maths test results B Ages C AFL football teams（澳式足球） D Heights of students in a class E Lengths of bacterium,Example 1,Which of the following is not discrete data? A Number of students older than 17.5 years old B Number of girls in a class C Number of q

9、uestions correct in a multiple choice test D Number of students above 180 cm in a class E Height of the tallest student in a class,EXAMPLE 2:,a whole number (countable).一个可以数的数，即整数,multiple choice mltipl tis选择题；,Categorical data ( 分类数据）is data split into two or more categories. Categorical data can

10、be: nominal（称名数据） data that can be arranged into categories but not ordered（此类数据可以进行分类单不需要排序） for example arranging shoes by colour or athletes by gender （举例：鞋子按颜色分类或者运动员按性别分类） ordinal （有序数据） data that can be arranged into categories that have an order, （此类数据可以进行分类但同时具有一定的顺序） for example levels of e

11、ducation from high school to post-graduate degrees. （举例：从高中到研究生学历的受教育水平）,nominalnmn()ladj. 名义上的；有名无实的；,ordinaldn()ladj. 顺序的，依次的 n. 数 序数,本课单词汇总,本课单词汇总,本课单词汇总,本课单词汇总,1 Which of the following is not numerical data? A Number of students in a class B The number of supporters at an AFL match C The amount

12、of rainfall in a day D Finishing positions in the Melbourne Cup E The number of coconuts on a palm tree,课堂练习,2 Which of the following is not categorical data? A Preferred political party B Gender C Hair colour D Salaries E Religion,课堂练习,3 Which of the following is not discrete data? A Number of play

13、ers in a netball team B Number of goals scored in a football match C The average temperature in March D The number of Melbourne Storm members E The number of twins in Year 12,课堂练习,4 Which of the following is not continuous data? A The weight of a person B The number of shots missed in a basketball g

14、ame C The height of a sunflower in a garden D The length of a cricket pitch E The time taken to run 100 m,课堂练习,5 Write whether each of the following represents numerical or categorical data. a The heights, in centimeters, of a group of children b The diameters, in millimeters, of a collection of bal

15、l bearings c The numbers of visitors to an exibit each day d The modes of transport that students in Year 12 take to school e The 10 most-watched television programs in a week f The occupations of a group of 30-year-olds,课堂练习,6 Which of the following represent categorical data? a. The numbers of sub

16、jects offered to VCE students at various schools （不同VCE学校的学生选课数量） b. Life expectancies （平均寿命） c. Species of fish (鱼的种类） d. Blood groups （血型) e Years of birth （出生的年份） f. Countries of birth（出生的国家） g. Tax brackets(纳税信用等级),练习,练习,8. An example of a numerical variable is: A attitude to 4-yearly elections（

17、4年一期的选举制） (for or against) B year level of students （学生的年级） C the total attendance at Carlton football matches（在卡尔顿足球比赛的总人次） D position in a queue at the pie stall （在饼档队列中的位置） E television channel numbers shown on a dial （在仪表盘中显示电视频道号码）,1.再次阅读书本1.2，补上相关单词的中文翻译 2.默写单词（写在默写本上） （先写音标，再默写英文三次，中文一次） 格式如右

18、： 3.完成课后1.2练习：T9-16， 写在练习本上。,作业：,A stem-and-leaf plot, or stem plot for short, is a way of ordering and displaying a set of data, 一个茎叶图，或者干图，是一种将一组数据进行排序和展示的方法。 with the advantage that all of the raw data is kept. 这种图的优势就在于保留了所有的原始数据 Since all the individual values of the data are being listed, it i

19、s only suitable for smaller data sets (up to about 50 observations). 由于所有的数据的个体值都被列出，所以它只适用于较小的数据集（最多约50个观测值）。,1.3 Stem plots,stem-and-leaf plot茎叶图,the raw data 原始数据,individual values个体值,suitable for适合于,Observations观测，观察,A stem-and-leaf plot, or stem plot for short, is a way of ordering and displayi

20、ng a set of data, 一个茎叶图，或者干图，是一种将一组数据进行排序和展示的方法。 with the advantage that all of the raw data is kept. 这种图的优势就在于保留了所有的原始数据 Since all the individual values of the data are being listed, it is only suitable for smaller data sets (up to about 50 observations). 由于所有的数据的个体值都被列出，所以它只适用于较小的数据集（最多约50个观测值）。,1

21、.3 Stem plots,The following stem plot shows the ages of people attending an advanced computer class.,1.3Stem plots,In cases where there are numerous leaves attached to one stem在一个茎上有许多叶子的情况下 (meaning that the data is heavily concentrated in one area), （这意味着数据集中在一个区域) the stem can be subdivided.茎可以被细

22、分 Stems are commonly subdivided into halves or fifths. 茎通常分为两半或五份 By splitting the stems, we get a clearer picture about the data variation. ） 通过分割的茎，我们得到一个更清晰的图片的数据变化。,细分的原则,attached to ttt tu: 附属于，隶属于,A stem plot is constructed by splitting the numerals of a record into two parts the stem, which i

23、n this case is the first digit, 茎表示第一位数 and the leaf, which is always the last digit. 叶表示第二位数,A stem plot,The number of cars sold in a week at a large car dealership over a 20-week period is given as shown. 16 12 8 7 26 32 15 51 29 45 19 11 6 15 32 18 43 31 23 23 Construct a stem plot to display the

24、 number of cars sold in a week at the dealership.,Example3,分三步进行： 1.先写出最大值highest，最小值lowest ，茎stem的数据,2.先分类抄写,3.由小到大重排，列出KEY,The masses (in kilograms) of the members of an Under-17 football squad are given as shown. 70.3 65.1 72.9 66.9 68.6 69.6 70.8 72.4 74.1 75.3 75.6 69.7 66.2 71.2 68.3 69.7 71.3

25、 68.3 70.5 72.4 71.8 Display the data in a stem plot.,Example 4,Subdivided再分，细分,Concentrated集中,Variation变异，变化,分析： In cases where there are numerous leaves attached to one stem (meaning that the data is heavily concentrated in one area), the stem can be subdivided. Stems are commonly subdivided into

26、halves or fifths. By splitting the stems, we get a clearer picture about the data variation.,分三步进行： 1.先写出最大值highest， 最小值lowest ， 茎stem的数据 2.先分类抄写 3.由小到大重排，列出KEY,A set of golf scores for a group of professional golfers trialing a new 18-hole golf course is shown on the following stem plot. Produce an

27、other stem plot for these data by splitting the stems into: a halves b fifths.,Example 5,Stem plots:练习,练习：The following data was collected from a company that compared the battery life (measured in minutes) of two different Ultrabook computers（超级笔记本电脑）. To complete the test they ran a series of prog

28、rams on the two computers and measured how long it took for the batteries to go from 100% to 0%.,a Draw a back-to-back stem plot (using the same stem) of the battery life of the two Ultrabook computers.,b Use the stem plot to compare and comment on the battery life of the two Ultrabook computers,Com

29、puter 1 lasts longer but is not as consistent. Computer 2 is more consistent but doesnt last as long. 搜索网络 计算机1持续时间较长，但不一致。计算机2是比较一致的，但不会持续太久。,本课单词,本课单词,本课单词,本课单词,认真阅读课本1.3，补上新单词的中文 记忆并默写单词本课单词，格式同前一课 完成课后1.3练习：T1，T3,T5,T8,T16,作业：,1.4 Dot plots, frequency tables and histograms, and bar charts点图，频率表，

30、柱状图，条形图,In dot plots, a single dot represents each data value. Dot plots are used to display discrete data where values are not spread out very much. They are also used to display categorical data. When representing discrete data, dot plots have a scaled horizontal axis and each data value is indica

31、ted by a dot above this scale. The end result is a set of vertical lines of evenly-spaced dots. 在点图中，一个点代表每个数据值。点图是用来显示离散数据的值是不是很分散。他们也被用来显示分类数据。当代表离散数据时，点图有一个缩放的水平轴，每个数据值表示由一个点以上这个规模。最终的结果是一组均匀分布的点的垂直的“线”。 A histogram is a useful way of displaying large data sets (say, over 50 observations). *直方图是一

32、种有用的方式显示大型数据集（说，超过50个观察）。 The vertical axis on the histogram displays the frequency and the horizontal axis displays class intervals of the variable (for example, height or income). *在直方图上的垂直轴显示的频率和水平轴显示的变量的类间隔（例如，高度或收入）。 The vertical bars in a histogram are adjacent with no gaps between them, as we

33、 generally consider the numerical data scale along the horizontal axis as continuous. *直方图中的垂直条是相邻的，它们之间没有间隙，因为我们通常认为沿水平轴的数值数据规模为连续的。Note, however, that histograms can also represent discrete data. It is common practice to leave a small gap before the first bar of a histogram. *请注意，但是，这个直方图也可以表示离散数据

34、。这是常见的做法，在直方图的第一条前留下一个小的差距。 When data are given in raw form that is, just as a list of figures in no particular order it is helpful to first construct a frequency table before constructing a histogram. *如果给出数据是原始数据，就是一个没有特定序列的罗列，先构建频率表对画直方图很有帮助。,课文重点内容翻译,适用于 1. display discrete data. 离散数据 2. display

35、 categorical data. 分类数据 具体画法 a scaled horizontal axis一个有刻度的水平轴 Draw a dot above this scale，indicates each data value 每个数据值用点表示,一、dot plots点图,The number of hours per week spent on art by 18 students is given as shown. 4 0 3 1 3 4 2 2 3 4 1 3 2 5 3 2 1 0 Display the data as a dot plot.,EXAMPEL 6,适用于 n

36、umerical data（ continuous ）连续的数值数据 注意： no gaps in horizontal direction水平方向没有间隙、缺口,二、Frequency tables and histograms频率表和柱状图,注意： 1、discrete data-a small gap 表示离散数据时，留一个小缺口 2、 raw data- frequency table 如果给出原始数据，先画频数表 3、table -histogram 如果给定表格，直接画柱状图,二、Frequency tables and histograms频数表和柱状图,The data bel

37、ow show the distribution of masses (in kilograms) of 60 students in Year 7 at Northwood Secondary College. Construct a frequency histogram to display the data more clearly. 45.7 45.8 45.9 48.2 48.3 48.4 34.2 52.4 52.3 51.8 45.7 56.8 56.3 60.2 44.2 53.8 43.5 57.2 38.7 48.5 49.6 56.9 43.8 58.3 52.4 54

38、.3 48.6 53.7 58.7 57.6 45.7 39.8 42.5 42.9 59.2 53.2 48.2 36.2 47.2 46.7 58.7 53.1 52.1 54.3 51.3 51.9 54.6 58.7 58.7 39.7 43.1 56.2 43.0 56.3 62.3 46.3 52.4 61.2 48.2 58.3,Example7,只给原始数据,Example 8,解释： 离散的数据，但是横轴上需要 一个组距，因此将数据左右各 延伸半个单位,给定频率表,A bar chart consists of bars of equal width separated by

39、 small, equal spaces and may be arranged either horizontally or vertically. Bar charts are often used to display categorical data. In bar charts, the frequency is graphed against a variable as shown in both figures. The variable may or may not be numerical. However, if it is, the variable should rep

40、resent discrete data because the scale is broken by the gaps between the bars.条形图由大小相等、可以水平或垂直排列的等宽度的组成的条形图。条形图通常用来显示分类数据。在条形图中，频数是相对于图形和数字所示的变量。变量可能是或可能不是数值。然而，如果它是，变量应该代表离散数据，因为刻度是由条形图之间的差距而产生。,三、Bar charts条形图,适用于： categorical data分类数据 或者discrete data离散数据,三、Bar charts条形图,适用于： Categorical data 分类数据

41、 注意： Percentages 用百分比数来显示数据 the total bar length represents 100% 整条线段表示100%.,四：Segmented bar charts分段条形图,步骤： 1、转化成比例 2、用100mm的矩形表示整体 3、分别画出每个的长度 4、写出表示的名称和数据,可以用不同颜色表示，也可以用不同底纹表示,Example9,适用于：直接用直方图很难处理， 数据比较大且各个值之间千差万别。,五：Using a log (base 10) scale用常用对数测量,130万 9万 227万 14万 14万 18万 8万 43万 4万 5万,We c

42、an then group our data using class intervals based on log values (from 4 to 7) to come up with the following frequency table and histogram.,Example 10,If we are given values in logarithmic form, by raising 10 to the power of the logarithmic number we can determine the conventional number. For exampl

43、e, the number 3467 in log (base 10) form is 3.54, and . = 3467. We can use this fact to compare values in log (base 10) form, as shown in the following worked example.,interpreting log (base 10) values,The Richter Scale measures the magnitude of earthquakes using a log (base 10) scale. How many time

44、s stronger is an earthquake of magnitude 7.4 than one of magnitude 5.2? Give your answer correct to the nearest whole number.,Example 11,Solution： 7.4 5.2 = 2.2 10 2.2 = 158.49 (correct to 2 decimal places) The earthquake of magnitude 7.4 is 158 times stronger than the earthquake of magnitude 5.2.,本

45、课单词,本课单词,本课单词,本课单词,阅读课本内容，查阅新单词，补充中文 抄默写新单词 课后练习：，,.作业,1.1-1.4 复习课,重点单词 离散， 连续， 数值数据， 分类数据， 有序数据， 称名数据， 茎叶图， 圆点图， 直方图， 条形图， 分段条形图， 频率表,重要方法： 区别各类数据 可数离散； 可测量连续 50个数据以内用茎叶图， 50个以上用频率表，直方图 千差万别的数据用取LOG（base10)来转变 分段条形图（利用百分比,1、The following table shows a variety of top speeds. The correct value, to 2

46、decimal places, for a cheetahs top speed using a log (base 10) scale would be: A 5.57 B 5.47 C 7.45 D 4.81 E 11.07,1.4练习课：11月30日,The table shows the flow rate of world famous waterfalls. Use this table to complete questions 1 and 2. Victoria Falls 1 088 m3/s Niagara Falls 2 407 m3/s Celilo Falls 5 4

47、15 m3/s Khane Phapheng Falls 11 610 m3/s Boyoma Falls 17 000 m3/s,练习,1 The correct value, correct to 2 decimal places, to be plotted for Niagara Fallsflow rate using a log (base 10) scale would be: A 3.38 B 3.0 4 C 4.06 D 4.23 E 5.10,2.The correct value, correct to 2 decimal places, to be plotted fo

48、r Victoria Falls flow rate using a log (base 10) scale would be: A 3.38 B 3.04 C 4.06 D 4.23 E 5.10,The number of hours spent on homework for a group of 20 Year 12 students each week is shown. 15 15 18 21 20 21 24 24 20 18 18 21 22 20 24 20 24 21 18 15 Display the data as a dot plot.,练习2,The number

49、of dogs at a RSPCA（皇家防止虐待动物协会） kennel each week is as shown. Construct a frequency table for these data. 7, 6, 2, 12, 7, 9, 12, 10, 5, 7, 9, 4, 5, 9, 3, 2, 10, 8, 9, 7, 9, 10, 9, 4, 3, 8, 9, 3, 7, 9 A. Using the frequency table in question above, construct a histogram by hand. B Using CAS construct

50、a histogram from the data,练习3：,The number of people who attended the Melbourne Grand Prix墨尔本大奖赛 are shown. Year 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Attendance (000s) 360 359 301 301 303 287 305 298 313 323 a Construct a bar chart by hand to display the data. b Use CAS to construct a ba

51、r chart and compare the two charts.,作业练习2：,复习1.1-1.4单词，理解并记忆 预习1.5-1.6 查阅单词， 巩固本课的计算器使用方法,作业：,The amount of food money (correct to the nearest 50 cents) received each week by students in a Grade 11 class 35 1、 2、Use CAS to draw the dot plots and histogram 3、 Describe the shape of the distribution of

52、 these data. 4、What conclusions can you reach about the amount of pocket money received weekly by this group of students?,回顾,本课单词,Symmetric distributions对称分布 The data shown in the histogram below can be described as symmetric.,1.5Describing the shape ofstem plots and histograms描述茎叶图和直方图的形状,There is

53、a single peak（一个单一的峰） and the data trail off on both sides of this peak in roughly the same fashion.（同样的方式 ）,The figure on the left shows data which are negatively skewed. The data in this case peak to the right and trail off to the left.,Skewed distributions偏态分布,The figure on the right shows positi

54、vely skewed data. The data in this case peak to the left and trail off to the right.,Example12,The number of nights per month spent interstate by a group of flight attendants is shown in the stem plot. Describe the shape of distribution of these data and explain what this tells us about the number o

55、f nights per month spent interstate by this group of flight attendants.,练习,Positively skewed. This tells us that most of the flight attendants in this group spend a similar number of nights (between 2 and 5) interstate per month. A few stay awaymore than this . And a very few stay away a lot more.,T

56、he following table shows the number of cars sold at a dealership over eight months. Month April May June July Aug Sep Oct Cars sold 9 14 27 21 12 14 1 0 18 a Display the data on a bar chart. b Describe the shape of the distribution of these data. c What does this sample data tell us about car sales

57、over these months? d Explain why the most cars were sold in the month of June.（参考澳大利亚时间）,练习,作业： 查阅单词 默写单词 完成1.5 作业题,Summary statistics are used because they give us an idea about: 1. where the centre of the distribution is？ 分布的中心在哪里？ 2. how the distribution is spread out？ 分布是如何分散的？ * Four summary st

58、atistics the median -the interquartile range -the range - the mode 唯一的前提： which require that the data be in ordered form before they can be calculated.,Summary statistics 汇总统计,1.6 本课单词,The median中位数 The median is the midpoint of an ordered set of data. Half the data are less than or equal to the median. 举例： The median of the data 2,4,6,8,10 is_ The median of the data 2,4,6,8 is_,1.6The median, the interquartile range,the range and the mode 中位数，四分位范围 ，范围，众数,如何在茎叶图中找中位数A stem plot provides a quick way of locating a median since the data in a stem plot are already ordered,Step 1. Write do