How do we use statistics?

When most people hear the word 'statistics' they run away because it sounds boring, but the truth be told statistics is our only way of delineating the real world. Statistics was developed as a means of trying to understand how data works. Let me count the ways . . .

Statistics often means the collection, analysis and interpretation of data. People think of statistics as pie charts and accounting tables, but the real use of statistics is in reconciling accuracy and precision.

Precision is how far down something can be measured. In a length measurement the precision of the instrument used to make the measurement is how small of units it can measure. In other words how many decimal places it can record. If the instrument determines centimeters, the precision would be how many fractions of a centimeter could the instrument determine. An example would be that it could measure down to a hundredth of a centimeter.

Accuracy is how well the instrument can do the same measurement. In other words, if I take ten measurements of the same thing, how repeatable is the measurement. For example, in this case the accuracy would be expressed as plus or minus one hundredth of a centimeter.

I was literally smacked in the head with these two concepts during my first lab of collage physics. The instructor told us that we would be measuring a block of wood. How hard could it be? I soon found out. We were given a wooden block and a caliper and told to determine the volume of the block of wood. Normally, most people would measure the width, length and height and multiply them together. But no, that's not how you do it. What you do is take several (10) measurements of the each of the block's dimensions and then determine the mean of the measurements and then the standard deviation. Finding the mean is simply taking the average of the measurements. The standard deviation has to be calculated. The standard deviation is the square root of the sum of the variation of the measurements from the average. So, what you do is subtract the average from the measurements, square the result and then add them and take the square root of the sum of the squares.

Standard deviation is a measure of the quality of data. It tells us how much variation is in the measurements. The larger the deviation is the poorer the data. If we plot a curve of the measurements we'll get what is considered a probability distribution. For a normal data distribution the curve is bell shaped, and there are all sorts of ways to appraise the quality of the data.

One of the problems connected with taking measurements is in trying to get a representative sample. This is where statistics can go wrong. A representative sampling is what is says: it's supposed to give one a good average value that represents the object one is measuring. This may require taking enough measurements or samples of the object to determine a good average value.

Probability is what it says: the possibility of obtaining an accurate measurement of an object, and that's reflected in how low the standard deviation is. Probability is also the possibility of how many throws of dice will win me a big pot of dough (cash). That's gambling.

Well, to get back to my lab class, I was asked what the caliper's zero point was, essentially when the instrument was closed tight. I said zero, and was reprimanded. What the instructor wanted was the precision. The answer should have been zero plus or minus 0.01 centimeters.

No measurement is perfect because we live in a world full of uncertainties. When someone says that it's 20 C outside what they should be saying is that it's 20.0 plus or minus .1 C. There is no such thing as an exact value. It may be very precise but it's never exact, and this is a very important concept because no measurement is exact.

Thanks for reading.