Question

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?

Answer 1

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


`\bar x = (1)/(n) \sum_(i=1)^n x_i`


`\sum_(i=1)^n x_i = n \bar x`

So if the average of all 92 is 7 the sum of those is
`92 * 7`

The average of the last two is 7.2 so their sum is
`2 * 7.2`

That means the sum of the first 90 is
`92 * 7 - 2 * 7.2`

so the average of the first 90 is


`(92 * 7 - 2 * 7.2)/(90) = 6.99556` cm