48 MEASUREMENTS 



Other but not identical. If only random variations affect the results, a 

 graph of a large series of measurements tends to follow the "normal" 

 curve in Fig. 4-7. The higher a point on the curve, the more frequently 

 that value is found. A sharper and steeper curve indicates a more precise 

 measurement. Precision of measurement refers to the closeness of agree- 

 ment among the various values. 



Fig. 4-7. The "normal curve" of error. Values being measured extend along the 

 horizontal axis, and the height of the curve at any point is an indication of the 

 frequency with which that value occurs. 



If the measurement is accurate, the numbers obtained cluster around 

 the real and true value. Some individual numbers will be larger, some 

 smaller, but taken together the set of numbers gives a useful estimate 

 of the true value. Measurements cannot be accurate without being rea- 

 sonably precise. If, in contrast, some systematic error exists in the meas- 

 uring technique, the estimate can be precise without being accurate. 

 If you failed to notice that someone who needed a piece of maple wood 

 had cut it from the end of your meter stick, you might make precise but 

 inaccurate measurements. 



Measurements in physics strive for precision, which is necessary for 

 accuracy. This is the goal in biology, also, but such precision is rarely 

 achieved because biological materials are inherently variable. Even so, 

 the variability of biological material is no adequate reason for not making 

 quantitative measurements. The biologist simply must realize that his 



