Wednesday, April 23, 2008

Finishing statistics

Today we looked at the 2006 question in statistics.
The main points points that we went over were:
calculating standard deviation
finding the mean using mid-interval values
producing histograms
For calculating the standard deviation you should format your work into columns, working out the differences from the mean, then the differences squared (then this value x the frequencies if applicable) etc. If doesn't matter if your work isn't in columns, as long as you follow the correct steps and show your work. As a rule of thumb, almost all your data should be within 2 std deviations above and below the mean. This means that the value of the std deviation should not be more than 1/2 the mean.
Whenever you are finding the mean value from a set of data you should check your answer to see if it is reasonable. The most common error when finding the mean of a frequency distribution is to divide by the number of categories instead of the sum of the frequencies. If you do this, your mean will be much too large and it should be obvious that you've made a mistake.
The purpose of histograms is to distribute data across uneven intervals. It is not a straightforward bar chart. You should write the frequency in a circle in each block. You can use the alternative format of histogram which has a key showing e.g. one square = 5 cars (in the 2006 question).

Homework for tonight is the 2005 statistics question. This one includes weighted mean and std deviation of a frequency distribution. If you can do the statistics questions from 2005 to 2007 you will have covered the topic pretty comprehensively.

On Friday in the double class 2nd period we will have a test (statistics + maybe lin programming also).
Tomorrow, once we have corrected the homework, we will go on to Linear Programming.

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