## Introduction

Grouped data are presented in frequency distributions rather than entering each observation individually. Given a set of data points:

X 1, X 2, . . . , X n,

with respective frequencies:

f 1, f 2, . . . , f n,

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 the Divide key 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

Display

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 divide

0.37

Standard Error of the mean