MHB -gre.qu.10 quantity on 2 means

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The discussion focuses on a mathematical problem involving the calculation of means from two sets of measurements. The initial values are given as a=2300 from 100 measurements and a+b=1350 from 50 additional measurements. The total sum of all measurements is calculated to be 3650, leading to an arithmetic mean of 73/3. It is noted that since there are more elements with a lower mean (23) than those with a higher mean (27), the overall arithmetic mean is less than 25. The conversation highlights the importance of careful setup to avoid errors in calculations.
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posted a screenshot because I think the wording is awkward and I think it is easy to setup it up wrong

so to begin with we have a and b being list of added numbers
$\dfrac{a}{100}=23$ and $\dfrac{a+b}{150}=27$

so now what?
 
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we have sum of 100 measurements = 2300

sum of 50 additional measurements = 27 * 50 = 1350

total sum = 2300 + 1350 = 2650

so arithmetic mean = $\frac{3650}{150} = \frac{73}{3}$

so B is bigger

for a short cut 25 is mean of 23 and 27

more elements(100) have mean 23 and less (50) elements have 27 so arithmetic mean < 25
 
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mahalo i probably would of missed it
 
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