Okay I'm doing a lab report, and I need to find the average of two trials. Can someone show me step-by-step how do find the uncertainty for this average:
(4.32g+4.17g)/2
=4.25
The values I used and their uncertainties:
4.32g +/- 0.02
4.17g +/- 0.02
To find the uncertainty for the average of two trials, you need to consider the uncertainties of the individual values. Here's a step-by-step explanation of how to calculate the uncertainty for the average:
1. Start by finding the average of the two values. In this case, you calculated the average as 4.25 g.
2. Next, find the difference between each individual value and the average. For the first value (4.32 g), the difference is 4.32 - 4.25 = 0.07 g. For the second value (4.17 g), the difference is 4.17 - 4.25 = -0.08 g (note the negative sign).
3. Take the absolute value of each difference to ensure positive values. So, the absolute difference for the first value is 0.07 g, and for the second value, it is also 0.08 g.
4. Now, determine the average uncertainty by adding the absolute differences and dividing by the number of trials (2 in this case). So, (0.07 g + 0.08 g) / 2 = 0.075 g.
5. The uncertainty for the average is the average uncertainty you just calculated. Therefore, the uncertainty for the average of (4.32g + 4.17g) / 2 is 0.075 g.
Remember, when calculating uncertainties, it's important to consider the systematic errors and the precision of the measuring instrument used. The provided uncertainties of ±0.02 g for each value account for the precision of the weighing instrument.