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What is the average (arithmetic mean) of the first 90 measurements in a certain list of 92 measurements? (1) the average of the 92 measurements is 7.0 centimeters. (2) the average of the last 2 measurements is 7.2 centimeters?

Respuesta :

DeanR
The sum of all the measurements is just the average times the number.

[tex]\bar x = \frac{1}{n} \sum_{i=1}^n x_i [/tex]

[tex] \sum_{i=1}^n x_i = n \bar x [/tex]

So if the average of all 92 is 7 the sum of those is [tex]92 \times 7[/tex]

The average of the last two is 7.2 so their sum is [tex]2 \times 7.2[/tex]

That means the sum of the first 90 is [tex]92 \times 7 - 2 \times 7.2[/tex]

so the average of the first 90 is

 [tex]\dfrac{92 \times 7 - 2 \times 7.2}{90} = 6.99556[/tex] cm



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