Question

Assume 5 independent measurements are made on the length of a rod, the measurements are: 4.8, 5.1, 5.0, 4.9, 5.2.

a) Find the average length of the rod.

b) Find the uncertainty in the avergae length of the rod.

c) Approximately how many measurements must be made ro reduce the uncertainty in the average length to .03?

Answer 1

a) Find the average length of the rod.

Sum of terms = 4.8 + 5.1 + 5.0 + 4.9 + 5.2 = 25 Number of terms 5 Sum of terms Number of terms Mean = Mean =- Mean5 25

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b) Find the uncertainty in the avergae length of the rod.

Step 1: Find the mean. [X In this example: X Step 2: Create the following table data - mean data-mean 0.2 0.1 data 0.04 0.01 5.1 5.0 4.9 5.2 0.01 0.2 0.04 Step 3: Find the sum of numbers in the last column to get. , Σ(n-x)-0.1 Step 4: Calculata variance using the above formula 0.1 ar

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c) Approximately how many measurements must be made ro reduce the uncertainty in the average length to .03?

n=5

Answer 2

a)average lemgth=4.8+5.1+5.0+4.9+5.2/5

=5

b) V = SUM[(x - m)^2]/N where the x's are your data values and m = SUM(x)/N is the average for N data points. Greater variance means greater uncertainty in your data points.

v=sum(5-1)^2/5

=5

V=0to reduce that number to 0.03 by taking some new number of measurements. Wouldn't I just use the ratio 0.03/5 = 0.006 and then multiply that by 5? So I would need to take 3, or 4, measurements to reduce my uncertainty to 0.03.