独家Alevel数学Statistic1S1考试知识点.doc

wordSummary of key points in S1 Chapter 1: Binomial distribution1. 〔重点***〕计算二项分布的概率： 〔1〕公式法〔**〕，由，如此有 〔2〕查表法〔***〕：利用书中135-139页中的，其中p 是0.05的倍数、一直到0.50，n最小是5、最大是502. 〔重点**〕计算二项分布的期望和方差：，如此有 3. 〔考点*〕二项分布的条件：l A fixed number of trials,.l Each trial should be success or failure.l The trials are independent.l The probability of success,, at each trial is constant. 其中，为指数〔index〕，为参数〔parameter〕难点是要求根据题意写出二项分布的条件，如果有题意背景的，要根据题意写。

4. 〔考点*〕如果，其中，如此，那么；如果p是0.05的倍数，如此可以用查表法求概率5. 典型例题：例7/8/9*/10/11/12/13(a)/14*6. 复习题：Review Exercise 1: 1/4/87. 练习册局部题目： 12-01-2, 10-01-1, 08-01-2Chapter 2: Representation and summary of data – location1、Frequency tables and grouped datacumulative frequency：to add a column to the frequency table showing the running total of the frequencies.A grouped frequency distribution consists of classes and their related class frequencies.Classes 30-31 32-33 34-35For the class 32-33Lower class boundaryUpper class boundaryClass width is 33.5-31.5=2Class mid-point 2、The measurements of location of the centre of a set of data – mode, median and meanl The mode is the value that occurs most often.l The median is the middle value or the half of the two middle values, when the data is put in order.l The mean is the sum of all the observations divided by the total number of the observations.The mean of a sample of data in a frequency distribution, is where 3、Coding for large data valuesCoding is normally of the form where and are to be chosen.To find the mean of the original data; find the mean of the coded data, equate this to the coding used and solve. Chapter 3:Representation and summary of data – measures if dispersion1、The range of a set of data is the difference between the highest and lowest value in the set.The quartiles, split the data into four parts. To calculate the lower quartile, divide by 4.For discrete data for the lower quartile, divide by 4. To calculate the upper quartile, divide by 4 and multiply by 3. When the result is a whole number find the mid-point of the corresponding term and the term above. When the result is not a whole number round the number up and pick the corresponding term.For continuous grouped data for divide by 4, fordivide by 4 and multiply by 3. Use interpolation to find the value of the corresponding term.The inter-quartile range is 2、The standard deviation and variance of discrete datavariance=standard deviation= If you let stand for the frequency, then and Variance=3、Adding or subtracting numbers does not change the standard deviation of the data.Multiplying or dividing the data by a number does affect the standard deviation.To find the standard deviation of the original data, find the standard deviation of the coded data and either multiply this by what you divide the data by, or divide this by what you multiplied the data by. Chapter 4: Representation of data1. A stem and leaf diagram is used to order and present data given to two or three significant figures. Each number is first split into its stem and leaf.Two set of data can be pared by using back-to-back stem and leaf diagrams.2、An outlier is an extreme value that lies outside the overall pattern of the data, which is n inter-quartile rangeorn less that the lower quartile inter-quartile range.3、Box plotUsing box plots to pare two sets of data4、HistogramA histogram gives a good picture of how data are distributed. It enables you to see a rough location, the general shape of the data and how spread out the data are.A histogram is similar to a bar chart but are two major differencesl There are no gaps between the bars.l The area of the bar is proportional to the frequency. To calculate the height of each bar (the frequency density) use the formula Area of bar=frequency. is the easiest value to use when drawing a histogram then Frequency density= 5、The shape (skewness) of a data setThe ways of describing whether a distribution is skewed:n You can use the quartiles. If then the distribution is symmetrical. If then the distribution is positively skewed. If then the distribution is negatively skewed.n You can use the measures of location mode=median=mean describes a distribution which is symmetrical. modemedian>mean describes a distribution with negative skew. 6、paring the distributions of data setsl The IQR is often used together with the median when the data are skewed.l The mean and standard deviation are generally used when the data are fairly symmetrical.Chapter 5: Probability1、Vocabulary used in probabilityA sample space is the set of all possible outes o。