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HP 48g Series Calculators - Grouped Statistics (Weighted Mean, Population Standard Deviation, and Sample Standard Deviation

Description
Grouped data are presented in frequency distributions to save time and effort in entering each observation individually. Standard Deviation is calculated on either a Population (entire population has been sampled) or Sample (only part of the population was sampled).
Given a set of data points ( X1, X2, X3, X4, . . .Xn ) with respective frequencies ( Y1, Y2, Y3, Y4, . . . Yn ), the following programs will calculate Weighted Mean, Population Standard Deviation, and Sample Standard Deviation. This data must be stored in the object 'SIGMADAT' as a 2 x n matrix. (E.g. [ [ X1 Y1 ] [ X2 Y2 ] . . . [Xn Yn ] ] ).
Calculator symbol key
The procedures in this document use the following text to represent symbol keys:
Key
Description
Text Representation
Right-shift key
RS
Left-shift key
LS
Move cursor left
cursor-left
Move cursor right
cursor-right
Move cursor up
cursor-up
Move cursor down
cursor-down
Backspace/clear
backspace
Program entry
  1. To store the following programs in the calculator, it is recommended to create a sub-directory called "GSTATS":
    1. Press RS, then MEMORY.
    2. Press NEW.
    3. Press cursor-down and enter a name into the NAME field.
    4. Highlight the _DIRECTORY check field, and press CHK (or +/-).
    5. Press OK.
  2. Change to the "GSTATS" directory and type in the first program using the program delimiters (< >). All characters must be entered exactly as shown in the example. Upper case must be upper case, spaces must be included; use the RS, then CHARS menu for characters not located on the keyboard. Then press ENTER to put the program on the stack. (See the User's Guide for more on programming the HP 48.)
  3. To store the program; press ['], then the program name (e.g. W, M, N, ENTER, then STO.
  4. Repeat steps 1, 2, and 3 for the other two programs.
Program use
  1. To run each program separately, key in the 2 x n matrix:
    1. Press RS, then MATRIX to use the MatrixWriter.
    2. Enter the data. Use a separate row for each individual record and a separate column for each variable within a record. For example, a data set containing the height, weight, and age for each of 100 people would be entered as 100 rows of three columns each.
    3. Press ENTER when finished entering the data.
    4. Enter a name for the data matrix onto level 1 of the stack and press STO OR On the command line, use the matrix delimiters [ ] (e.g. [ [ X1 Y1 ] [ X2 Y2 ] . . . [ Xn Yn ] ] ) and press ENTER
  2. To store the data; press ['], RS, SIGMA, D, A, T, ENTER, then press STO
  3. Press the menu key in the VAR menu that corresponds to the required program.
Program - GSTAT
The following optional program gives an input window that contains a field for data and a list of the above programs.
Optional input window
Use the same procedure above for keying in the following program:
Then, simply press the menu key for GSTAT in the VAR menu and the following screen will appear:
Figure : Grouped Statistics screen
Press RS, then MATRIX to use the MatrixWriter, or press EDIT to access the data on the command line. Key in a Y or an N for each of the Grouped Statistics programs.
Example of calculating standard deviation
A survey of 266 one-bedroom apartment rentals reveals that 54 rent for $390 per month, 32 rent for $395 per month, 88 rent for $400 per month, and 92 rent for $406 per month. What is the average monthly rent per apartment and the standard deviation? The data in the MatrixWriter should look like this:
Figure : MatrixWriter screen for standard deviation example
The correct answers are:
Figure : Correct answers for standard deviation example
The answers in the above screen are shown in Standard mode. To get an answer in a different display mode (e.g. 2 or 3 places), perform the following steps:
  1. Press RS, then MODES
  2. Highlight the NUMBER FORMAT field.
  3. Press CHOOS (or, press +/- repeatedly to cycle through the fixed list of options, and stop when the desired option appears in the field).

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