Home Table of Contents About the Authors Glossary Buy This Book Joseph Henry Press


SOLUTION TO EXERCISE 3

back to exercise

intro: TOC for Knowledge Concepts, Exercises, and Solutions



A graph is useful in this situation.  The graph should have
"number of measurements" on the vertical axis, and "luminosity" on 
the horizontal axis.  

(a) The mean value of the luminosity measurements is about 208 units. 
This is also about the place where the most measurements are, which is
around 210 units; this agreement gives us additional confidence
So the best estimate of the luminosity of Venus is about 208 units. 

(b) The bell curve that best fits the distribution of measurements 
is about 30 measurements high at 208 units; so the half-maximum level 
is 15 measurements.  The bell curve intersects 15 at about 195 units 
and 225 units; so the full-width at half maximum (FWHM) is about 30 units.
Remember that you're measuring the width of the bell curve, and not
necessarily the width of the data point distribution.

(c) The margin of error is +/- half of the FWHM, that is 15 units.
This is a ratio of 208 +/- 15 units, or +/- (15/208) or +/- 7.2 percent.