## hba 2 years ago Stats help required

1. hba

2. hba

Actually i know. $Mean=\sum_{}^{}fx/\sum_{}^{}f$ I know, $\sum_{}^{}f=2000$

3. sami-21

4. hba

I also think that is the answer as i tried doing it.

5. hba

But here x1,x2,x3 cannot be 8.5,7.5 and 8 because it is actually the mean

6. hba

As mentioned in the ques

7. wio

Okay give me a second.

8. hba

Sure

9. wio

Now suppose that we call $\sum fx$The 'total'

10. wio

We want the 'total' of each sub population.

11. wio

12. wio

To get the 'total' of the whole population.

13. wio

From there we can find the mean of the whole population.

14. ParthKohli

We know that the sum is $$700 \times 8.5 + 800 \times 7.5 + 500 \times 8$$

15. hba

No No No 8.5,7.5 and 8 cannot be x

16. hba

They are the means

17. wio

Yeah, but he's not using that formula.

18. ParthKohli

Since mean is sum of observations divided by number of observations, we know that the sum of observations multiplied by the number of observations is the sum of observations.

19. wio

He using this: $\sum fx = \frac{\sum fx}{\sum f}\times \sum f$

20. ParthKohli

Can you continue from this point?

21. sami-21

i don't think there is any problem with taking them as x's . what you alreadyy did is correct 7.975 .

22. ParthKohli

lunch... g2g

23. hba

But how can you say mean of x is actually x?

24. sami-21

(8.5*700 + 800*7.5 + 500*8)/2000

25. sami-21

these are different random variables for the whole population . you can just use them in the formula .

26. hba

27. hba

It says that it is the mean @sami-21

28. wio

Okay so if you have three means... suppose they are $$m_1, m_2, m_3$$

29. wio

$m_1 = \frac{\sum_1fx}{\sum_1f}$

30. sami-21

yes it does says . and requires the mean for population . which should be taking the means of the sub populatiions .

31. hba

One more thing,If that is not the formula,What is it?

32. hba

@xoya Shu away

33. wio

the mean of all three will be: $m_4 = \frac{\sum_4 fx}{\sum_4x} = \frac{\sum_1 fx + \sum_2 fx+ \sum_3 fx}{\sum_1 f + \sum_2 f + \sum_3 f}$

34. wio

This is because the total frequency $$\sum_4 f$$ is the sum of the sub frequencies. The total weight $$\sum_4 fx$$ is equal to the sum of all the weights.

35. wio

Notice how $m_1 = \frac{\sum_1 fx}{\sum_1 f} \implies m_1\sum_1 f = \sum_1 f x$

36. hba

Okay so what would the formula basically?

37. hba

be*

38. wio

Given means... $$m_1, m_2, \dots$$ with total frequencies $$f_1,f_2,...$$ then the mean of the totals is: $\frac{\sum m_if_i}{\sum f_i}$

39. hba

Thanks a lot :D :D

40. wio

It's not the same formula, they just happen to be the same though by coincidence.

41. hba

I see.