Double Matrix Method
Transcript
双矩阵方法。在一些更复杂的阵容中，
人口的每个成员一次按两种方式分类。例如，如果我们要查看特定公司的员工，
we might group employees by gender, either male or female. And education, and here we're just gonna consider two categories.
只有大学学位，即学士学位与高级学位。 In that example, every single employee would be classified by gender. Also, every single employee would be classified by education level. 所以每个人都会立即分为两种方式。问题可能给出的信息可能是多少女性和 of course that would include both education levels.
Or it might be how many folks with advanced degrees and of course that would include both males and females. 或者它可能是非常具体的，例如有多少员工是具有高级学位的女性。 So the question could give us any of those pieces of information. It could also ask for any of those pieces of information.
所以这里有很多信息。所以让我们通过看这个问题来开始：在300名员工的公司， 120 are females. A total of 200 employees have advanced degrees and the rest have college degree only. If 80 employees are males with college degrees only, 有多少女性具有高级学位？
Well, we're not gonna solve this just yet. Here's what I'm gonna say. 请注意，某些信息相对较快地达到其他信息。 We know there are 300 employees. 120 are females that means the other 180 have to be males.
同样，如果员工200人有高级程度。那么那么必须有100个大学度。 So, there's certainly ways that some pieces of information lead to others but we need a way to organize all of this information. 组织在这种问题中的信息的优秀方法被称为双矩阵方法。
这使得使用矩阵，即矩形框阵列，每个盒子都有一个数字。 列代表一个v的类别ariable, and the rows will represent the categories of the other variable. For this problem let's say that gender will be the columns and education level will be the rows.
So, here's the tricky part. There are two genders so we will need three columns. 一个用于女性，一个男性，一个用于总计，男性加女性。还有两个教育水平，所以我们需要三行。 只有大学，只有一个用于高级学位，而且为总计。所以完整的系统，这里是象征性的形式。
We have again, the columns are the genders, the rows have the education levels. A，B，C和D是原始数据。所以B将是具有高级学位的女性。 C would be the males who have a college degree only. Those are the raw data.
E and F are the row totals. We add across the rows to get everything on the right. So A plus C equals E. B plus D equals F. E would be the total number of people with a college degree only. So that would be males and females.
F would be the total number of people with an advanced degree only. Again, that would be males plus females. G and H are the column totals. So we add down to get everything at the bottom. A plus B equals G. C plus D equals H.
So G would be the total number of females, H would be the total number of males. In both those cases, 我们只是将所有程度的水平集中在一起。最后是T，那个底部右侧盒子，是总计。 这是整个公司的每个人，集合中的每个人。我们可以通过添加底行来获得，G Plus H等于T.
或者我们可以在右图中添加，E Plus F等于T.等等，一切都应该检查。 All those sums should be equal. So, now try this question again and then we'll solve it with the double matrix method. You can pause the video here.
好的。 所以问题上有四个数字，我要写下我们的双矩阵。 所以现在正如我们上面所说的那样，如果有120名女性，必须有180个男性，以便他们加起来300。
Similarly, if there are 200 with advanced degrees there must be 100 with college degree onlys. 再一次，所以他们加起来最多300.现在看起来沿着男行。 We have 80 plus blank equals 180. So what has to go in that blank?
Obviously 100. There must be 100 males with advanced degrees. So that 80 plus 100 equals 180. Well, now look across the advanced degree category. We have blank plus 100 equals 200. So clearly, this has to be 100 also.
There must be 100 females with advanced degrees. That's the answer for which we're looking. Let's just check and make sure that this works. We look down the female column, blank plus 100 should equal 120 so 这意味着这等于20.然后我们在跨越该顶行20加80等于100。
Everything checks and so indeed there are 100 females with advanced degrees in this company. 如果其中一个变量有三类需要四个，或者 four rows or four columns. Because again, we'd need one for each category as well as one for the total.
Of course, the information can be given in simple numerical form as we had in the last problem or in some other form, ratios or algebraic. Something like that. There's many different ways that the numbers can be given. 这是一个相对挑战性的问题。所以暂停视频，然后我们会谈论这个。
好的。 在一定的学校，有80名新生，100个大二学生和220名高年级学生，从三个城市中汲取。 好的。所以首先，80,100和220，这些是不同等级的总数。
We have grade level is one of our categories so it has one of our variables, it has three categories. 我们在这三个类别中的每个类别都有总计。然后我们有三个城市。 那将是另一个变量。学生来自哪个城市？
我们有三个类别。我们在这里提供百分比信息。 60来自A，60％，来自B的30％，其余来自C.然后我们有其他一些信息。 来自C的所有学生都是新生。来自B的一半学生是高年级学生， 其余部分在另外两个等级之间均匀分开。
How many sophomores are from A? So for this we need an enormous double matrix table, and here I've written in the totals for freshmen, sophomore, and upperclassmen. And I just went ahead and summed across that bottom row to get 400. 所以，这是学校的人数。所以现在我们可以开始考虑百分比信息。
60% of the students are from A. We need 60% of 400. Well, 10% of 400 is 40. So multiply that by six and that's 240. 那是60％。然后30％来自B.
井30％只有60％的一半，所以一半的240分为120. 30加60是90，因此这意味着最后10％来自C. So 10% of 40, 400 of course is just 40. So now we have all the row totals and column totals. 然后我们有这么大的信息。来自C的所有学生都是新生。
So there are 40 students from C. All 40 of them are freshmen. And then we can just put zeroes in these columns. So that enormously simplifies everything. Now we're told that half the students from B are upperclassmen. So half of 120 is 60.
其中一半是高年级学生。而另一个60均匀分开，所以30和30。 所以现在我们想要A.我们希望俯视二年级学生。 We have blank plus 30 plus 0 equal 100. Clearly this number has to be 70, and that's our answer.
The double matrix method can enormously simplify problems in which each member is 放入两种不同的类别。行总和中的条目在最右侧列中的行总计。 The entries in the columns sum to the column totals in the bottom row. And the grand total, in the lower right-hand box, is everyone.
This equals the sum of the row totals and it also equals the sum of the column totals.
Read full transcript
只有大学学位，即学士学位与高级学位。 In that example, every single employee would be classified by gender. Also, every single employee would be classified by education level. 所以每个人都会立即分为两种方式。问题可能给出的信息可能是多少女性和 of course that would include both education levels.
Or it might be how many folks with advanced degrees and of course that would include both males and females. 或者它可能是非常具体的，例如有多少员工是具有高级学位的女性。 So the question could give us any of those pieces of information. It could also ask for any of those pieces of information.
所以这里有很多信息。所以让我们通过看这个问题来开始：在300名员工的公司， 120 are females. A total of 200 employees have advanced degrees and the rest have college degree only. If 80 employees are males with college degrees only, 有多少女性具有高级学位？
Well, we're not gonna solve this just yet. Here's what I'm gonna say. 请注意，某些信息相对较快地达到其他信息。 We know there are 300 employees. 120 are females that means the other 180 have to be males.
同样，如果员工200人有高级程度。那么那么必须有100个大学度。 So, there's certainly ways that some pieces of information lead to others but we need a way to organize all of this information. 组织在这种问题中的信息的优秀方法被称为双矩阵方法。
这使得使用矩阵，即矩形框阵列，每个盒子都有一个数字。 列代表一个v的类别ariable, and the rows will represent the categories of the other variable. For this problem let's say that gender will be the columns and education level will be the rows.
So, here's the tricky part. There are two genders so we will need three columns. 一个用于女性，一个男性，一个用于总计，男性加女性。还有两个教育水平，所以我们需要三行。 只有大学，只有一个用于高级学位，而且为总计。所以完整的系统，这里是象征性的形式。
We have again, the columns are the genders, the rows have the education levels. A，B，C和D是原始数据。所以B将是具有高级学位的女性。 C would be the males who have a college degree only. Those are the raw data.
E and F are the row totals. We add across the rows to get everything on the right. So A plus C equals E. B plus D equals F. E would be the total number of people with a college degree only. So that would be males and females.
F would be the total number of people with an advanced degree only. Again, that would be males plus females. G and H are the column totals. So we add down to get everything at the bottom. A plus B equals G. C plus D equals H.
So G would be the total number of females, H would be the total number of males. In both those cases, 我们只是将所有程度的水平集中在一起。最后是T，那个底部右侧盒子，是总计。 这是整个公司的每个人，集合中的每个人。我们可以通过添加底行来获得，G Plus H等于T.
或者我们可以在右图中添加，E Plus F等于T.等等，一切都应该检查。 All those sums should be equal. So, now try this question again and then we'll solve it with the double matrix method. You can pause the video here.
好的。 所以问题上有四个数字，我要写下我们的双矩阵。 所以现在正如我们上面所说的那样，如果有120名女性，必须有180个男性，以便他们加起来300。
Similarly, if there are 200 with advanced degrees there must be 100 with college degree onlys. 再一次，所以他们加起来最多300.现在看起来沿着男行。 We have 80 plus blank equals 180. So what has to go in that blank?
Obviously 100. There must be 100 males with advanced degrees. So that 80 plus 100 equals 180. Well, now look across the advanced degree category. We have blank plus 100 equals 200. So clearly, this has to be 100 also.
There must be 100 females with advanced degrees. That's the answer for which we're looking. Let's just check and make sure that this works. We look down the female column, blank plus 100 should equal 120 so 这意味着这等于20.然后我们在跨越该顶行20加80等于100。
Everything checks and so indeed there are 100 females with advanced degrees in this company. 如果其中一个变量有三类需要四个，或者 four rows or four columns. Because again, we'd need one for each category as well as one for the total.
Of course, the information can be given in simple numerical form as we had in the last problem or in some other form, ratios or algebraic. Something like that. There's many different ways that the numbers can be given. 这是一个相对挑战性的问题。所以暂停视频，然后我们会谈论这个。
好的。 在一定的学校，有80名新生，100个大二学生和220名高年级学生，从三个城市中汲取。 好的。所以首先，80,100和220，这些是不同等级的总数。
We have grade level is one of our categories so it has one of our variables, it has three categories. 我们在这三个类别中的每个类别都有总计。然后我们有三个城市。 那将是另一个变量。学生来自哪个城市？
我们有三个类别。我们在这里提供百分比信息。 60来自A，60％，来自B的30％，其余来自C.然后我们有其他一些信息。 来自C的所有学生都是新生。来自B的一半学生是高年级学生， 其余部分在另外两个等级之间均匀分开。
How many sophomores are from A? So for this we need an enormous double matrix table, and here I've written in the totals for freshmen, sophomore, and upperclassmen. And I just went ahead and summed across that bottom row to get 400. 所以，这是学校的人数。所以现在我们可以开始考虑百分比信息。
60% of the students are from A. We need 60% of 400. Well, 10% of 400 is 40. So multiply that by six and that's 240. 那是60％。然后30％来自B.
井30％只有60％的一半，所以一半的240分为120. 30加60是90，因此这意味着最后10％来自C. So 10% of 40, 400 of course is just 40. So now we have all the row totals and column totals. 然后我们有这么大的信息。来自C的所有学生都是新生。
So there are 40 students from C. All 40 of them are freshmen. And then we can just put zeroes in these columns. So that enormously simplifies everything. Now we're told that half the students from B are upperclassmen. So half of 120 is 60.
其中一半是高年级学生。而另一个60均匀分开，所以30和30。 所以现在我们想要A.我们希望俯视二年级学生。 We have blank plus 30 plus 0 equal 100. Clearly this number has to be 70, and that's our answer.
The double matrix method can enormously simplify problems in which each member is 放入两种不同的类别。行总和中的条目在最右侧列中的行总计。 The entries in the columns sum to the column totals in the bottom row. And the grand total, in the lower right-hand box, is everyone.
This equals the sum of the row totals and it also equals the sum of the column totals.
