# Statistics Functions

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1 Statistics Functions The HP-11C calculator provides functions to perform one or two variable statistical calculations. The data samples are entered into the calculator using the [ +] key, which automatically calculates statistics sums and store them in the Storage Registers from 0 to 5 (called the Statistics Registers ): Register Sum Description 0 n Number of data samples. 1 x Summation of x-values. 2 x 2 Summation of squares of x-values. 3 y Summation of y-values. 4 y 2 Summation of squares of y-values. 5 x y Summation of products of x and y-values. One Variable Statistics In one-variable statistical calculations, enter each data point (the X-value ) by keying in the X-value and pressing [ +]. Each time you press [ +] the calculator does the following: Adds 1 to the number in R0 and displays the number of samples entered. The X-value is added to the number in R1. The square of the X-value is added to R2. Two Variable Statistics In two-variable statistical calculations, enter each data pair (the X and Y-values ) by typing the Y-value into the display, pressing [ENTER], then type in the X-value and finally press [ +]. Each time you press [ +] the calculator does the following:

2 Adds 1 to the number in R0 and displays the number of samples entered. The X-value is added to the number in R1. The square of the X-value is added to R2. The Y-value is added to the number in R3. The square of the Y-value is added to R4. The product of the X and Y-values is added to R5. The Calculator s functions involved in the statistics calculations are: Keys [g] [ ẍ ] [g] [ s ] [f] [ ŷ,,r ] [f] [L.R.] [RCL] [ +] Description Calculates the means (arithmetic averages) of the X and Y- values. The mean of the X-values appears in the display; to display the mean of the Y-values, press [X Y]. Calculates the standard deviation of the X and Y-values. The standard deviation of the X-values appears in the display. To display the standard deviation of the Y-values, press [X Y]. Calculates a linear estimation of a new Y-value given a X-value. The new Y-value appears in the display. To display the correlation coefficient (R²) of the regression, press [X Y]. Calculates the coefficients A (slope) and B (y-intercept) of the linear regression equation Y = A X + B. The slope A -value is placed in the stack-y and the y-intercept B -value is placed in the stack-x register. Recalls the content of R3 ( y values) to the stack-y and R1 ( x values) to the stack-x [f] clear [ ] Clears the statistic registers R0 to R5 and the stack.

3 Correcting Accumulated Statistics: If the data was entered incorrectly, the accumulated statistics can easily be corrected. Simply key in the incorrect data point or data pair again and press [g] [ -] to subtract the incorrect data from the statistic registers. Then enter the correct data point or data pair and press [ +]. Each time you press [g] [ -] the calculator does the following: Subtracts 1 from the number in R0 displaying the new number of samples. The x-value is subtracted from the number in R1. The square of the x-value is subtracted from R2. The y-value is subtracted from the number in R3. The square of the y-value is subtracted from R4. The product of the x and y-values is subtracted from R5. Example of Statistic Calculations Enter the following data samples : Year Coal Production (Billion Metric Tonnes) Electric Ouput (Billions of MWh) Solution: [f] clear [ ] Clears statistics registers [ENTER] [ +] First sample entry [ENTER] [ +] Second sample entry.

4 1.792 [ENTER] [ +] Third sample entry [ENTER] [ +] Fourth sample entry [ENTER] [ +] Fifth sample entry. Based on the data entered, do the following: Calculate the accumulated statistics of the data Correct the 1.943, data pair to 1.946, Calculate the Mean of the corrected data. Calculate the Standard Deviation of the corrected data. Perform a Linear Regression and obtain the equation that relate the coal production with the electricity output. Estimate the coal production for an energy output of Keystrokes to find the accumulated statistics : [RCL]  Sum of X-values ( x) from register 1. [RCL]  Sum of squared X-values ( x 2 ) from register 2. [RCL]  Sum of Y-values ( y) from register 3. [RCL]  Sum of squared Y-values ( y 2 ) from register 4. [RCL]  Sum of the product of X-values and Y-values ( x y) from register 5. Keystrokes to correct the data and calculate the mean and standard deviation : [ENTER] [g] [ -] Subtract the wrong data pair from the accumulated statistics [ENTER] [ +] Add the correct data to de accumulated statistics. [g] [ ẍ ] Calculates the mean of X-values (electric output).

5 [X Y] Show the mean of Y-values (coal production). [g] [ s ] Standard deviation of X-values (electric output). [X Y] Standard deviation of Y-values (coal production). Keystrokes to get the linear regression and do the estimation : [f] [L.R.] Calculates the y intercept (the value of y when x = 0). [X Y] Shows the slope of the linar regression. Linear Regression Equation: Coal Production = (Electric Output) [f] [ ŷ,,r ] Estimated coal production for electric output. [X Y] Correlation coefficient (R 2 ). As a special feature, the RLM-11CX calculators have a convenient tool to create and edit statistical X,Y data samples. To show it, press the OPT key, and in the 2) Statistics: section, touch the Input X,Y Data, or in the 6) Utilities: section, touch the X,Y Data Editor. After a X,Y data list is created with the above tools, you can use specific menu in section 2) Statistics: to perform advanced statistics calculations and curve fitting models.

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