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hba
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hba
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Actually i know.
\[Mean=\sum_{}^{}fx/\sum_{}^{}f\]
I know,
\[\sum_{}^{}f=2000\]
sami-21
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do you have the answer key
is the answer 7.975 ???
hba
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I also think that is the answer as i tried doing it.
hba
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But here x1,x2,x3 cannot be 8.5,7.5 and 8 because it is actually the mean
hba
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As mentioned in the ques
wio
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Okay give me a second.
hba
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Sure
wio
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Now suppose that we call \[
\sum fx
\]The 'total'
wio
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We want the 'total' of each sub population.
wio
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Then we can add them
wio
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To get the 'total' of the whole population.
wio
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From there we can find the mean of the whole population.
ParthKohli
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We know that the sum is \(700 \times 8.5 + 800 \times 7.5 + 500 \times 8\)
hba
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No No No 8.5,7.5 and 8 cannot be x
hba
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They are the means
wio
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Yeah, but he's not using that formula.
ParthKohli
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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.
wio
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He using this: \[
\sum fx = \frac{\sum fx}{\sum f}\times \sum f
\]
ParthKohli
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Can you continue from this point?
sami-21
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i don't think there is any problem with taking them as x's .
what you alreadyy did is correct
7.975 .
ParthKohli
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lunch... g2g
hba
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But how can you say mean of x is actually x?
sami-21
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(8.5*700 + 800*7.5 + 500*8)/2000
sami-21
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these are different random variables for the whole population . you can just use them in the formula .
hba
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@wio Please justify
hba
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It says that it is the mean @sami-21
wio
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Okay so if you have three means... suppose they are \(m_1, m_2, m_3\)
wio
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\[
m_1 = \frac{\sum_1fx}{\sum_1f}
\]
sami-21
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yes it does says . and requires the mean for population . which should be taking the means of the sub populatiions .
hba
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One more thing,If that is not the formula,What is it?
hba
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@xoya Shu away
wio
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the mean of all three will be: \[
m_4 = \frac{\sum_4 fx}{\sum_4x} = \frac{\sum_1 fx + \sum_2 fx+ \sum_3 fx}{\sum_1 f + \sum_2 f + \sum_3 f}
\]
wio
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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.
wio
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Notice how \[
m_1 = \frac{\sum_1 fx}{\sum_1 f} \implies m_1\sum_1 f = \sum_1 f x
\]
hba
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Okay so what would the formula basically?
hba
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be*
wio
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Given means... \(m_1, m_2, \dots \) with total frequencies \(f_1,f_2,...\) then the mean of the totals is: \[
\frac{\sum m_if_i}{\sum f_i}
\]
hba
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Thanks a lot :D :D
wio
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It's not the same formula, they just happen to be the same though by coincidence.
hba
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I see.