# Experimental Errors And Uncertainty Brett Spencer

**Topics:**Statistics, Standard deviation, Arithmetic mean

**Pages:**8 (1323 words)

**Published:**June 25, 2015

Experiment 4: Experimental Errors and Uncertainty

Brett R. Spencer

Date Performed: June 10th, 2015: 3:10 p.m.

PHY 111C02

Section 1: Experiment and Observation

Time, t (s)

Dist. Y1 (m)

Dist. Y2 (m)

Dist. Y3 (m)

Dist. Y4 (m)

Dist. Y5 (m)

Mean of Y

Standard Dev.

t^2

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.50

1.00

1.40

1.10

1.40

1.50

1.28

0.22

0.25

0.75

2.60

3.20

2.80

2.50

3.10

2.84

0.30

0.56

1.00

4.80

4.40

5.10

4.70

4.80

4.76

0.16

1.00

1.25

8.20

7.90

7.50

8.10

7.40

7.82

0.36

1.56

A. Objective

The objective of this lab consists of gaining perspective and understanding of experimental errors and uncertainty in the parameters of physical measurements.

B. Equipment Used

Experimental Errors and Uncertainty Experiment Manual

Computer with Excel 2010

Pens/Pencils

Paper (plain and graph)

C. Data

Data Table 1 shows 5 different variable data sets along with a constant set speed in order to test the variables. Measurements were taken during a free-fall experiment, where the distance travel (y) was recorded at each 4 depicted times (x). The calculations for the average speed for each team slot, along with its standard deviation were manually calculated to three significant figures. The results related to distance, however, were not rounded in any format.

Section 2: Analysis

A. Calculations

The average (or mean) of a data set is the most common and useful known measurements when determining central tendency. By calculating the mean, there is a structure, advantageous approach to organizing and depicting either discrete or continuous data. The equation below helps determine this statistic:

Or, in denoted fashion:

The mean, for Sample A (0.5 seconds) was calculated as follows:

= (1.00 + 1.40 + 1.10 + 1.40 + 1.50) = 1.28

5

The standard deviation was also an important tool when determining how the data set is ultimately distributed. It helps prove whether or not the data is grouped closely together, or spread apart, which eventually leads into the calculation for percentage error and uncertainty with the trials. The equation below helps determine this statistic:

For example, Sample A’s (0.5 seconds) standard deviation was calculated as follows:

= √[(1.00-1.28)^2 + (1.40-1.28)^2 + (1.10-1.28)^2 + (1.40-1.28)^2 + (1.50-1.28)^2 = 0.22

Motion of a falling object starting from rest was also a key calculation in helping us determine, eventually, percentage error. The equation, y = 1/2 gt^2, where g is acceleration due to gravity, directly correlation into finding this statistic. When the data set associated with the mean of Y was allocated and compared to the data in set t^2 in a graph format, we were able to construct a trend line with a slope of 4.94x. We then used the above equation as follows:

1/2g = the slope of the trend line, therefore g = 2 x (4.94) = 9.88

We then used this data to determine percentage error. The equation for this statistic is shown below:

%Error = |Experimental Value – Accepted Value| x 100

Accepted Value

In this case, accepted value was determined to be 9.8 m/s^2. Therefore percentage error was calculated as:

%Error = |9.88-9.8| x 100 = .816%

9.8

B. Graphs

Figure 1 shows the relation between the mean of Y versus time (t).

Figure 2 shows the relationship between the mean of Y and t^2.

C. Error Analysis

The error percentage in this case helped depicted the level of uncertainty between the projected rate of acceleration due to gravity (9.8) versus the experimental, or actual rate (9.88). This percentage is able to show how accurately our accepted value was depicted when compared to the factual data. The calculation (see above section) displayed our information being >1% off, sitting at .816%. It was...

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