If one has more than a few points on a graph, one should calculate the uncertainty in the slope as follows. In the picture below, the data points are shown by small, filled, black circles; each datum has error bars to indicate the uncertainty in each measurement. It appears that current is measured to +/- 2.5 milliamps, and voltage to about +/- 0.1 volts. The hollow triangles represent points used to calculate slopes. Notice how I picked points near the ends of the lines to calculate the slopes!

- Draw the "best" line through all the points, taking into
account the error bars.
Measure the slope of this line.
- Draw the "min" line -- the one with as small a slope as you
think reasonable (taking into account error bars),
while still doing a fair job of representing
all the data.
Measure the slope of this line.
- Draw the "max" line -- the one with as large a slope as you
think reasonable (taking into account error bars),
while still doing a fair job of representing
all the data.
Measure the slope of this line.
- Calculate the uncertainty in the slope as one-half of the difference between max and min slopes.

In the example above, I find

147 mA - 107 mA mA "best" slope = ------------------ = 7.27 ---- 10 V - 4.5 V V 145 mA - 115 mA mA "min" slope = ------------------ = 5.45 ---- 10.5 V - 5.0 V V 152 mA - 106 mA mA "max" slope = ------------------ = 9.20 ---- 10 V - 5.0 V V mA Uncertainty in slope is 0.5 * (9.20 - 5.45) = 1.875 ---- V

There are at most two significant digits in the slope, based on the uncertainty. So, I would say the graph shows

mA slope = 7.3 +/- 1.9 ---- V

* Last modified 7/31/2007 by MWR. *

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.