>> I'm going to show you the answer to this, by doing it in a spreadsheet. You
could do all of these calculations, without any technology. And if you did that,
that's really great. It's always really good practice to calculate things
without using any technology, but just for the purposes of figuring out the
standard deviation, technology can really speed along this process. So I'm not
going to use any shortcuts here. We're going to do it exactly as we would if we
didn't have technology. So first we need to take the avearage of all of these,
we're going to sum them up. So we're taking the sume of all of these. I could
also just write equals a1 plus a2 plus a3 all the way to a10. And we'd get the
same thing. But why would we do that if we can simply write this. Now to take
the average all we do is divide by the number of values which is 10. So that's
just going to be 51,511.1. Alternatively, the nice thing about technology is we
can just do this. Take the sum, and divide by the total number. Do it all in 1
step. So now we have the average. Now we're going to subtract the average from
each 1 of these values. Not the opposite, where we subtract each of these values
from the mean. That's an important distinction. In this case, it doesn't matter
as much but in other statistical concepts that's an important distinction to
make. So we'll write equals A1 minus. The mean. So I'm subtracting the mean from
each of these values. Now I could just do the same thing here and write equals
a2 minus the mean but that would be tedious. We can just drag this down. When
you do that, remember that there has to be a little plus sign there. That means
you're successfully dragging it down. If you went like this, it won't do
anything. It'll just highlight the boxes. So here, we have the deviations from
the mean. Here, in the next column We're going to square each deviation. Equals
b1 squared. And again, we're going to drag it down. So we have the squared
deviations for each of these values. Now remember that the variance is the
average squared deviation. So we could just write. Average of c1 to c10. But I
want to make sure we go through all the other steps in between. So let's again
practice calculating the average just for clarity's sake. So the variants then
would be the sum of c1 to c10. Remember that's how you start out taking the
average, and then divide by 10. So here's the variance, and then the standard
deviation is simply the square root of the variance. So we'll write equals SQRT.
That's the shortcut for square root. And then we can just see C13. So we know
that the standard deviation is 6557.16 approximately. Now I want to point out
something really important before we finish this solution video. Here I simply
said equals square root of this cell C13. Whereas here, I wrote out the
whole average. The reason for that is because say I had but this all here, A13.
Then, when we drag it down, we don't get the right deviations. And we can double
click on it, and see what it did. Here, it took A4 minus A16, whereas here it
took A1 minus A13, which is what we wanted. But we want it to always stay A13,
which is why we have to make sure this is a constant. And the way to make sure
it's a constant is by just writing it. Notice also that all of these values
changed when these values changed because all these values are dependent of
these values So when we change it back we should again get the correct standard
deviation.
>> I'm going to show you the answer to this, by doing it in a spreadsheet. You
could do all of these calculations, without any technology. And if you did that,
that's really great. It's always really good practice to calculate things
without using any technology, but just for the purposes of figuring out the
standard deviation, technology can really speed along this process. So I'm not
going to use any shortcuts here. We're going to do it exactly as we would if we
didn't have technology. So first we need to take the avearage of all of these,
we're going to sum them up. So we're taking the sume of all of these. I could
also just write equals a1 plus a2 plus a3 all the way to a10. And we'd get the
same thing. But why would we do that if we can simply write this. Now to take
the average all we do is divide by the number of values which is 10. So that's
just going to be 51,511.1. Alternatively, the nice thing about technology is we
can just do this. Take the sum, and divide by the total number. Do it all in 1
step. So now we have the average. Now we're going to subtract the average from
each 1 of these values. Not the opposite, where we subtract each of these values
from the mean. That's an important distinction. In this case, it doesn't matter
as much but in other statistical concepts that's an important distinction to
make. So we'll write equals A1 minus. The mean. So I'm subtracting the mean from
each of these values. Now I could just do the same thing here and write equals
a2 minus the mean but that would be tedious. We can just drag this down. When
you do that, remember that there has to be a little plus sign there. That means
you're successfully dragging it down. If you went like this, it won't do
anything. It'll just highlight the boxes. So here, we have the deviations from
the mean. Here, in the next column We're going to square each deviation. Equals
b1 squared. And again, we're going to drag it down. So we have the squared
deviations for each of these values. Now remember that the variance is the
average squared deviation. So we could just write. Average of c1 to c10. But I
want to make sure we go through all the other steps in between. So let's again
practice calculating the average just for clarity's sake. So the variants then
would be the sum of c1 to c10. Remember that's how you start out taking the
average, and then divide by 10. So here's the variance, and then the standard
deviation is simply the square root of the variance. So we'll write equals SQRT.
That's the shortcut for square root. And then we can just say C13. So we know
that the standard deviation is 6557.16 approximately. Now I want to point out
something really important before we finish this solution video. Here I simply
said equals square root of this cell C13. Whereas here, I wrote out the
whole average. The reason for that is because say I had but this all here, A13.
Then, when we drag it down, we don't get the right deviations. And we can double
click on it, and see what it did. Here, it took A4 minus A16, whereas here it
took A1 minus A13, which is what we wanted. But we want it to always stay A13,
which is why we have to make sure this is a constant. And the way to make sure
it's a constant is by just writing it. Notice also that all of these values
changed when these values changed because all these values are dependent of
these values So when we change it back we should again get the correct standard
deviation.
Vou mostrar a resposta fazendo um gráfico.
Você poderia calcular tudo isso sem nenhuma tecnologia, e se o fez,
ótimo.
É sempre uma boa prática fazer cálculos
sem usar tecnologia, mas para o propósito de descobrir
o desvio padrão, a tecnologia pode agilizar o processo.
Então não vou usar nenhum atalho aqui.
Faremos exatamente como faríamos se não tivéssemos tecnologia.
1º, vamos tirar a média de tudo isso,
então vamos somá-los.
Então somamos tudo isto.
Eu poderia apenas escrever "=a1 + a2 + a3" até 10,
e teríamos o mesmo.
Mas por que fazer isso quando podemos escrever só isso?
Para tirar a média, tudo o que fazemos é dividir pelo número de valores, que é 10.
Então será 51.511,10.
Como alternativa,
o bom da tecnologia é que podemos fazer só isso.
Pegar a soma e dividir pelo número total.
Tudo em um só passo.
Agora temos a média.
Agora vamos subtrair a média de cada um desses valores.
Não o oposto, onde subtraímos cada valor da média.
É importante diferenciar.
Neste caso, não importa tanto,
mas em outros conceitos estatísticos é importante diferenciar.
Então escrevemos "=a1-" e a média.
Então estou subtraindo a média de cada um desses valores.
Agora poderia fazer o mesmo aqui e escrever
"=a2- " e a média, mas seria um tédio.
Podemos só arrastar isto para baixo.
Quando fizer isso, lembre que precisa ter um sinal de mais ali.
Isso significa que você está mesmo arrastando para baixo.
Se fizer assim, não adianta.
Vai só selecionar os espaços.
Então aqui temos os desvios da média.
Aqui, na próxima coluna vamos elevar cada desvio ao quadrado.
"=b1" ao quadrado.
E de novo, arrastamos para baixo.
Então temos os desvios quadráticos de cada valor desses.
Lembre-se de que a variância é o desvio quadrático médio.
Então poderíamos escrever "média" de C1 a C10,
mas quero que façamos todos os passos intermediários.
Então vamos praticar calcular a média só para ficar claro.
Então as variáveis seriam a soma de C1 a C10.
Lembre-se que é assim que começa a tirar a média,
depois divida por 10.
Então aqui está a variância,
e o desvio padrão é simplesmente a raiz quadrada da variância.
Então escrevemos "=SQRT".
É o atalho para raiz quadrada.
E depois podemos ver C13.
Então sabemos que o desvio padrão é aproximadamente 6.557,16.
Quero falar de algo muito importante antes de terminarmos esta resolução.
Aqui eu só coloquei "=SQRT" desta célula C13.
Mas aqui, escrevi toda a média.
Isto porque, digamos que eu tivesse colocado esta célula aqui, A13.
Quando arrastássemos para baixo, não teríamos os desvios certos.
E podemos clicar duas vezes e ver o que ele fez.
Aqui, ele pegou A4 menos A16,
enquanto aqui, pegou A1 menos A13, que é o que queríamos.
Mas queremos que continue A13,
por isso temos que nos certificar de que isto seja uma constante.
Para isso, basta escrevê-lo.
Note também
que estes valores mudaram quando esses outros mudaram,
porque estes valores dependem desses outros.
Então ao mudar de volta,
devemos ter novamente o desvio padrão correto.
我要在电子表格内解答这道题
你可以在不使用任何技术手段的情况下完成所有计算
如果你已完成所有计算 这很不错
计算时不使用任何技术手段 总是很好的做法 但为了得出标准偏差
运用技术手段其实可以加快计算过程
因此这里我不会使用任何捷径 如果没有技术手段可用
我们会尽其所能完成计算 首先需得出所有这些数的平均数
再求出它们的和 取所有这些数的和
我也可以写成 = a1 + a2 + a3 … a10
将得出相同的结果 但是如果能直接写出结果 为什么还要进行那样的步骤呢
要得到平均值 只需除以值的数量10
结果是51511.1 或者也可以采用技术手段 其好处是
我们只需这样做 取其和值后再除以总数
整个计算过程在1步内完成 我们得到平均值
每个值减去平均值 而不是平均值减去每个值
这两者的区别很大 假若这样 虽关系不大
但在其它统计概念中 那是很显著的区别
写出 = A1 减平均值 这就是我从每个值减去平均值的原因
我也可以在这里做相同的操作并写出 =a2- 平均值
但太繁琐 我们可以下拉它
下拉后 记住那里有一个小加号
表明你成功下拉 如果你照这样操作
表格不会有任何变化 只会突出显示框格 这里我们得出平均值的偏差
下一步我们将求出每个偏差的平方
= b1 的平方 我们再一次下拉
得出每个值的偏差平方 记住方差是平均值的平方偏差
我们可以写出 c1 到 c10 的平均值
我想确保我们完成了之间的所有步骤
为了清楚起见 让我们再一次练习计算平均值
方差应是 c1 到 c10 的和 记住那就是取平均值的方法
然后再除以10 这里得出了方差
标准偏差就是方差的平方根 我们在这里输入 = SQRT
那就是求平方根的缩写 然后我们再输入 C13
我们知道标准偏差大约为6557.16
完成这个解题视频之前 我想指出一个重点
这里我只说 =(C13) 的平方根 而这里我写出
整个平均值 原因是这里我只有 A13
当我们下拉时 我们无法得到正确的偏差 我们可以双击
看出现什么 这里出现了 A4 减去 A16
而这里出现了 A1 减去 A13 但我们想让它始终是 A13
这就是为什么一定要确保这是一个常数的原因
确保它是一个常数的方法是写出常数 还要注意的是这些值变化时
所有这些值也会变化 因为所有这些值取决于这些值
改回来时 我们再次得到正确的
标准偏差