Lab : 20 Measurements



Lab : 20 Measurements

Lab Assignment:

1. Obtain a small ruler of about 6 inches in length. Choose two well defined points on a wall, table, floor, or any surface about 4 to 6 feet apart from each other.

2. With the ruler, measure this straight line distance with the ruler. When taking the distance reading, read the ruler to the first interpolated digit. For example if the ruler is in eights of an inch, interpolate to sixteenths.

3. Repeat the measuring process 20 times. This is your sample of 20 repeated measurements of a distance.

4. Calculate the sample mean, and standard deviation. Identify any blunders (outliers) lying outside a 3 sigma rejection limit. After taking these out of your sample, recompute the sample mean and standard deviation. Any blunders?

5. Analyze your sample data to determine whether you have a normal distribution.

a. Plot a histogram, using five equal-width intervals. Interpret this diagram to see if the data's normally distributed.

1. Is the histogram a bell shaped curve? How close to ideal??

2. Inspect your dataset to see if you have the same number as + as – residual errors. Conclude?

3. Calculate the number of readings within 1 sigma of the mean, within 2 sigma of the mean, and within 3 sigma. Compute the percent of your total sample lying within each of these intervals. Compare these percents with the theoretical percent for a normal distribution. Conclude?

b. Demonstrate the "law of compensation in the mean". Plot your data means on a chart, taking your data one at a time (a mean of one, n=1). Plot your data means taking your data two at a time (n=2). Plot your data means averaging your data four at a time (n=4). Plot your data means averaging your data five at a time (n=5). Plot your data means averaging 10 at a time (n=10). Plot the mean of all 20 (n=20). The plot's horizontal axis is the number of readings in the mean (1, 2, 4, 5, 10, 20). The vertical axis is the value of the mean.

Also calculate and plot the theoretical curve of the "law of compensation in the mean." where sigma m = sigma /SQRT(n)

# of Data Pts 20 10 5 4 2 1

Value theoretical std error in mean

overall mean

1 2 4 5 10 20

Number in Mean

Analyze this chart and conclude whether there is any compensation evident in the means of your data. ??? Do you have about 2/3 of your means inside the theoretical lines? Discuss.

6. Compute the Least Squares Adjusted value for your 20 redundant measurements.

U = Sum (Xi – Xadj)^2

You are to find the least squares adjusted value by trial and error. Pick a trial adjusted value Xadj near the middle region of the measured values. Subtract this from each reading and then square the difference. Add all 20 squared differences for the quantity "U". Then try another trial adjusted value, compute U. Try another, compute U. Keep trying till you find the value that gives the minimum U. That's the "least sum of squares" adjusted value. See if your value compares in value with any other value that we used in this lab.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download