下面，百利天下小编为大家分享的是GRE数学数据分析视频讲解，希望对大家有帮助。
数据分析考查内容：1. Graphical Methods for Describing Data;2. Numerical Methods For Describing Data;3. Counting Methods;4. Probability;5. Distributions of Data, Random Variables and Probability Distributions;6. Data Interpretation Examples
1. Graphical Methods for Describing Data
Frequency Distributions(频率分布)
Relative Frequency Distributions: (相对频率分布)the associated frequency divided by the total number of data. (in terms of percents, fractions, or decimals)
例： A survey was taken to find the number of children in each of 25 families. A list of the values collected in the survey follows.
1 2 0 4 1 3 3 1 2 0 4 5 2 3 2 3 2 4 1 2 3 0 2 3 1
Bar Graphs(条形图)
A commonly used graphical display for representing frequencies, or counts, is a bar graph, or bar chart.
2. Numerical Methods For Describing Data
Measures of Central Tendency( 集中趋势测量)
Measures of Central Tendency indicate the “center” of the data along the number line.
(i) the arithmetic mean—usually called the average or simple the mean
(ii) the median
中位数及其计算
To calculate the median of n numbers, first order the numbers from least to greastest.
If n is odd, then the median is the middle number in the ordered list of numbers.
If n is even, then there are two middle numbers, and the median is the average these two numbers.
众数
The mode of a list of numbers is the number that occurs most frenquently in the list.
值域
The range of the numbers in a group of data is the difference between the great number G in the data and the least number L in the data; that is, G-L.
例：11, 10, 5, 13, 21, the range of the numbers is ————
答案：21-5=17。
standard deviation
方差：表示随机变量与它的数学期望之间的平均偏离程度的一个量。
计算公式为：一组数据中的每一个数与这组数据的平均数的差的平方和再除以数据的个数
标准方差就是方差的平方根。
Theory: the more the data are spread away from the mean, the greater the standard deviation; and the more the data are clustered around the mean, the lesser the standard deviation.
例：For the five data 0, 7, 8, 10, and 10, the standard deviation can be ————
the mean of the data is 7;
the squared differences 49, 0, 1, 9, 9;
the average of the five squared differences is 13.6.
the standard deviation can be 3.7.
例： Six hundred applicants for several post office jobs were rated on a scale from 1 to 50 points. The ratings has a mean of 32.5 points and a standard deviation of 7.1 points.how many SD above or below the mean is a rating of 48 points? a rating of 30 points?a rating of 20 points?
解答： Let d be the standard deviation, so d=7.1 points. Note that 1 standard deviation above the mean is 32.5+d=32.5+7.1=39.6 and 2 standard deviation above the mean is 32.5+2d=46.7, 32.5+xd=48 (x=2.2)
To summarize:
48 points is 15.5 points above the mean, or approximately 2.2 standard deviations above the mean.
30 points is 2.5 points above the mean, or approximately 0.4 standard deviations above the mean.
20 points is 12.5 points above the mean, or approximately 1.8 standard deviations above the mean.
Theory:
In any group of data, most of the data are within about 3 standard deviations above or below the mean.
Sets and Lists (集合和列表)
Sets集合
Members/elements数值/元素
Lists列表
Finite sets有限集合
Infinite sets无限集合
Subset子集
Empty sets孔集
Disjoint/Mutually exclusive两个集合没有交集
Venn diagram 韦恩图
Venn diagram is a useful way to represent two or three sets and their possible intersections and unions.
In a Venn diagram, sets are represented by circular regions that overlap if they have elements in common but do not overlap if they are disjoint.
The sets A, B and C are represented in the Venn diagram below, where U reprensents a universal set.
The regions with vertical stripes represent the set
the regions with horizontal stripes represent the
The region with both kinds of stripes represents the set
The sets B and C are mutually exclusive, often written
运算公式
Multiplication Principle
1. Suppose there are two choices to be made sequentially and that the second choice is independent of the first choice.
2. Suppose also that there are K different possibilities for the first choice and m different possibilities for the second choice.
3. The multiplication principle states under those conditions, there are Km different possibilities of the pair of choices.
例：A meal is to be ordered from a restaurant menu and that the meal consists of one entrée and one desert. If there are 5 entrees and 3 deserts on the menu,then there are————different meals that can be ordered from the menu.
答案是15种。
例： Suppose that a computer password consists of four characters such that the first character is one of the digits from 0 to 9 and each of the next 3 characters is any one of the uppercase letters from the 26 letters of the English alphabet.
How many different passwords are possible ?
分情况考虑：
(10)(26)(26)(26)=175,760
(10)(26)(25)(24)=156,000
以上就是GRE数学数据分析视频讲解的全部内容，希望对考生复习GRE数学有帮助。
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