**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 |
---|---|---|

| 1.00 | Calculator cleared and first data point entered |

| 2.00 | Second data point entered |

| 3.00 | Third data point entered |

| 4.00 | Fourth data point entered |

| 199.44 | Average monthly rent. |

| 5.97 | Standard Deviation |

| 0.37 | Standard Error of the mean |

Updated On: 12.07.14