Difference between revisions of "1988 AHSME Problems/Problem 29"
m |
(Added a solution with explanation) |
||
| (One intermediate revision by one other user not shown) | |||
| Line 13: | Line 13: | ||
==Solution== | ==Solution== | ||
| − | + | Apply one of the standard formulae for the gradient of the line of best fit, e.g. <math>\frac{\frac{\sum {x_i y_i}}{n} - \bar{x} \bar{y}}{\frac{\sum {x_{i}^2}}{n} - \bar{x}^2}</math>, and substitute in the given condition <math>x_3 - x_2 = x_2 - x_1</math>. The answer is <math>\boxed{\text{A}}</math>. | |
| − | |||
== See also == | == See also == | ||
{{AHSME box|year=1988|num-b=28|num-a=30}} | {{AHSME box|year=1988|num-b=28|num-a=30}} | ||
| − | + | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 15:03, 27 February 2018
Problem
You plot weight 
against height 
for three of your friends and obtain the points
. If 
and 
,
which of the following is necessarily the slope of the line which best fits the data?
"Best fits" means that the sum of the squares of the vertical distances from the data points to the line is smaller than for any other line.
Solution
Apply one of the standard formulae for the gradient of the line of best fit, e.g. 
, and substitute in the given condition 
. The answer is 
.
See also
| 1988 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 28 |
Followed by Problem 30 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
