HP 33s Scientific manual Summation Values and the Statistics Registers, Summation Statistics

xˆ , and

Normalizing Close, Large Numbers

The calculator might be unable to correctly calculate the standard deviation and linear regression for a variable whose data values differ by a relatively small amount. To avoid this, normalize the data by entering each value as the difference from one central value (such as the mean). For normalized x–values, this difference

must then be added back to the calculation of x andyˆ and b must also be adjusted. For example, if your x–values were 7776999, 7777000, and 7777001, you should enter the data as –1, 0, and 1; then add 7777000 back to

xand xˆ . For b, add back 7777000 ⋅ m. To calculate yˆ , be sure to supply an x–value that is less 7777000.

Similar inaccuracies can result if your x and y values have greatly different magnitudes. Again, scaling the data can avoid this problem.

Effect of Deleted Data

Executing {does not delete any rounding errors that might have been generated in the statistics registers by the original data values. This difference is not serious unless the incorrect data have a magnitude that is enormous compared with the correct data; in such a case, it would be wise to clear and reenter all the data.

Summation Values and the Statistics Registers

The statistics registers are six unique locations in memory that store the accumulation of the six summation values.

Summation Statistics

Pressing gives you access to the contents of the statistics registers:

„Press {Q} to recall the number of accumulated data sets.

„Press {º} to recall the sum of the x–values.

„Press {¸} to recall the sum of the y–values.

„Press {;º}, {;¸}, and {;º¸} to recall the sums of the squares and the sum of the products of the x and y — values that are of interest when performing other statistical calculations in addition to those provided by the calculator.

11–10Statistical Operations