Purpose:

This will complete our discussion of error and scientific notation.

1. Error

By performing measurements in class we have seen the difficulty in making measurments and also the inherent variability of the data.
We looked at actual seismograms to measure the distance between minute marks.  We saw that the measurements were affected by the width of the lines, the degree to which the paper is flat on the recording drum, as well as the experience of the observer.

We can use some simple relations of statistics to characterize the observations:

Number of obervations  - this will be unique ot each row

Mean  - this is the average of all observations

      Example: If I have  3 observations, e.g.,  1, 4 and 9, then the  Mean is computed on a calculator by  the operation

            Mean =  ( 1 + 4 + 9 ) / 3  where the 1,4,9 are the three observations, and the 3 is the Number of observations

Standard Error - this is an indication in the spread of observations - to compute this I need the Mean, so for our example we have

            Std Error = sqrt [  { (1-Mean)*(1-Mean) + ( 4 - Mean)*(4-Mean)  + (9-Mean)*(9-Mean) } / ( 3 - 1 ) ]
                    The 3 in the denominator is the number of observations, the -1 is required in the definition

     If you have a lot of samples,  66% shoud  lie with in Mean - Std Error and Mean + Std Error, and
     95% should lie within ( Mean - 2*Std Error) and ( M + 2*Std Error), and about 99 % between Mean +- 3 Std Error

Std Error of Mean - this is a measure of the stability of the means

           Std Error Mean = Std Error / sqrt (Number of obervations)

Assignment:

Given the following observations, determine the mean, standard error and standard error of the mean for these measurments of the number of millimeters (mm) per minute on the NHIL seismogram.  The units of the Mean, Standard Error and Standard Error of the Mean will be mm.

Data Set 1. (units in mm): 60.0, 60.5, 60.2, 58.5, 58.5, 61.0


Data Set 1:   Mean = ____________ (mm)  Standard Error = ______________ (mm) Standard Error of Mean = ______________ (mm)

Data Set 2. (units in mm): 60.0, 59.5, 60.5, 60.5, 60.0, 60.5

Data Set 2:   Mean = ____________ (mm)  Standard Error = ______________ (mm) Standard Error of Mean = ______________ (mm)

Statistically, 95% of the observed data should lie within Mean  +- Standard Error, for each data set, and

Statistically, 95% of the independent estimates should line within Mean +- Standard Error of Mean

2. Scientific Notation and SI Units

The following problems address physical units, scientific notation and some simple, but essential concepts.
  1. Given a resistor with a value of 12000 Ohns, write this value in Scientific Notation ______________ and in SI Units ___________
  2. The radius of the Earth is about 6371 km. Express this number is meters ___________________
  3. The density of  the upper mantle is about 3.3 gm/cm3 . Express this number in  kg/m3 ____________________
  4. Convert 3 hours 55 minutes and 20 seconds to seconds _________________
  5. If you travel 5 hours at a speed of 65 miles/hour, the distance traveled is ____________________ miles.
  6. If you you leave at 10:45 in the morning and travel 5 1/2 hours, what time do you arrive at your destination? ________________
  7. If you must be somewhere at 6:00 PM, and you must travel 10 1/4 hours to get there, when must leave? ____________________
  8. Express 1,234,567.89  in scientific notation. _______________________
  9. Express  0.012345 in scientific notation.  __________________________
  10.  If you have an iPod nano, with 8GB sotrage, and if the typical song consists of 4,000,000 bytes, what is the number of songs that can be stored? __________________
  11. If your new computer has a 100 GB disk drive, and if the comptuer can transfer 10 MB per second, how long will it take the computer to read the entire 100 GB? __________________________ (sec) = _______________________  (minutes)