## 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:

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

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 **divide**

0.37

Standard Error of the mean