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HP 12c Calculator - Mean, Standard Deviation, and Standard Error for Grouped Data

Introduction

Grouped data are presented in frequency distributions rather than entering each observation individually. Given a set of data points:
X1, X2, ...,Xn
with respective frequencies:
f1, f2, ...,fn
this procedure computes the mean, standard deviation, and standard error of the mean.

Instructions

Follow these steps to compute the mean, standard deviation, and standard error of the mean:
  1. Press f, then CLEAR [REG].
  2. Key in the first value and press ENTER twice.
  3. Key in the respective frequency and press STO, [+], 0, [X], then Sigma +. The display shows the number of data points entered.
  4. Repeat steps 2 and 3 for each data point.
  5. To calculate the mean (average) press RCL, 0, STO, 1, RCL, 6, STO, 3, g, then x-mean (the zero key).
  6. Press g, then s to find the standard deviation.
  7. Press RCL, 0, g, the Square Root key, then ÷ to find the standard error of the mean.

Example

A survey of 266 one-bedroom apartment rentals reveals that 54 rent for $190 per month, 32 rent for $195 per month, 88 rent for $200 per month, and 92 rent for $206 per month. What are the average monthly rental, the standard deviation, and the standard error of the mean?
Keystrokes (RPN mode)
Display
Comments
f, CLEAR [REG], 190, ENTER, ENTER, 54, STO, [+], 0, [X],then Sigma +
1.00
Calculator cleared and first data point entered
195, ENTER, ENTER, 32, STO, [+], 0, [X], then Sigma +
2.00
Second data point entered
200, ENTER, ENTER, 88, STO, [+], 0, [X], then Sigma +
3.00
Third data point entered
206, ENTER, ENTER, 92, STO, [+], 0, [X], then Sigma +
4.00
Fourth data point entered
RCL, 0, STO, 1, RCL, 6, STO, 3, g, then x-mean
199.44
Average monthly rent
g, then s
5.97
Standard Deviation
RCL, 0, g, square root, then ÷
0.37
Standard Error of the mean

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