2.1.6 Graphical Treatment of Errors and Uncertainties

Question 1

What is the best way to calculate gradient?

Answer 1

Use the largest possible triangle - points as far appt as possible; within the boundaries of the question to reduce percentage error.

Question 2

Produce and define three ways that one might use to reduce error on a graph.

Answer 2

1. Percentage error: the difference between two values divided by the average and shown as a percentage.
2. Error bars: these represent the absolute uncertainty in measurements and can be plotted in the x and y directions to get an error box.
3. A line on minimum and maximum acceptable worst fit - these have the min and max gradients that the error boxes will allow.

Question 3

Name the 6 stage process to find uncertainty in gradient.

Answer 3

1. Add error bars/ boxes to each point. The size of these is usually the same for each point;
2. Draw and calculate the gradient of the line of best fit, excluding outliers and making it go through as many points as possible - exual no. of pts above and below.
3. Draw line of worst fit;
4. Express as a positive value: MODULUS
   uncertainty = gradient of best fit - gradient of worst fit
5. Calculate percentage uncertainty:
   %unc = unc/gradient of best fit line x100
   OR
   Draw two lines of worst fit. Unc = half difference between max and min gradients.

Question 4

What is the process to find the uncertainty in the y intercept from the max/ min gradients? If you didn’t have a y axis intercept, what would you do?

Answer 4

1. Extrapolate all THREE lines of fit through y axis, so get ‘best’ & worst values of y axis intercept.
2. To find unc in y value, do highest value - lowest;
3. Plug numbers into %uncertainty = uncertainty/ ‘best’ y-intercept value x100
4. If didn’t have an intercept, would sub in values of gradients of both lines of worst fit into y=mx+c - find c and work forwards from stage 2.