The following information provides details on how the 2015 ACS 1-Year Standard Quality 40th Percentile Recent Mover Gross Rent of
**$1,006** was developed for Madison, WI HUD Metro FMR Area using the publicly releasable distributions from the 2015 ACS.

The standard quality Recent Mover Gross Rents that HUD uses in generating FMRs are derived from rent distributions
that are prohibited from public release under Title XIII to protect the
confidentiality of respondents. The distributions used in this demonstration
are rounded versions of the actual, protected data.

The rounding scheme is as follows:

0, count = 0

1 to 7, count = 4

all other counts are rounded to the nearest 5 (e.g., 10, 15, 20, 25, etc.)

Calculations using the rounded data may not produce the same result as calculations
using the protected data. The difference between HUD's actual results and those
demonstrated here is inversely related to the size of the area. That is,
the larger the area, the closer the calculation based on the
rounded data is likely to be to the Census base rent computed from the protected data.

"Standard Quality" units and rents are determined by limiting the
full ACS sample by including only responses meeting the following criteria:

a. Occupied rental units paying cash rent

b. Specified renter – on 10 acres or less

c. With full plumbing

d. With full kitchen

e. Not constructed in the last 2 years from the survey date

f. Meals not included in rent

The 2015 ACS did not included a question that could be used to filter public or assisted housing from the rental distributions, however HUD is required to ensure that FMRs exclude non-market rental housing in their computation. Therefore, HUD excludes all units falling below a specified rent level determined from public housing rents in HUD's program databases as likely to be either assisted housing or otherwise at a below-market rent (perhaps due to quality problems not otherwise captured by the survey questions).

The "public housing" rent cut-off for **Madison, WI HUD Metro FMR Area** in 2015 is $315.

The following table and calculations demonstrate how the 40th percentile 2015 ACS
standard quality Recent Mover Gross Rent is determined for **Madison, WI HUD Metro FMR Area**
using the public distribution of standard quality Recent Mover Gross Rents.

Portion of Standard Quality Recent Mover Gross Rent Distribution | Gross Rent Dollar Range | Number of Units | Percent of Eligible Distribution | Cumulative Percent |
---|---|---|---|---|

Units below interval containing public housing rent level of $315 |
$0 to $300 | 0 | Not in Distribution | Not in Distribution |

Units in interval containing public housing rent level of $315 |
$301 to $314 | 0.00 | Not in Distribution | Not in Distribution |

$315 to $349 | 0.00 | 0.0% | 0.0% | |

Units below interval containing 40th percentile standard quality Recent Mover Gross Rent of $1,021 |
$350 to $999 | 6,570 | 37.5% | 37.5% |

Units in interval containing 40th percentile standard quality Recent Mover Gross Rent of $1,021 |
$1,000 to $1,249 | 5,105 | 29.2% | 66.7% |

Units above interval containing 40th percentile standard quality Recent Mover Gross Rent of $1,021 |
$1,250 or more | 5,825 | 33.3% | 100.0% |

Total Units Above Public Housing Rent in Standard Quality Recent Mover Gross Rent Distribution | 17,500.00 |

There were no standard quality 2-bedroom units in the rent interval containing the Public Housing Rent level of $315.

The 40th percentile standard quality Recent Mover Gross Rent for **Madison, WI HUD Metro FMR Area** is computed by linear
interpolation over the 5,105 units in the rent range
$1,000 to $1,249. Linear interpolation
uses the assumption that the 5,105 units' rents are uniformly distributed
in the rent range around the 40th percentile.
Under this assumption, the proportion of the rent interval ($250)
that needs to be added to the lower limit of the interval to reach the 40th percentile rent
is the same as the proportion of units in the interval that needs to be added to the units in lower rent intervals
to reach 40 percent of units in the distribution.

40 percent of units = .4 x 17,500.00 = 7,000.00

Units below the 40th percentile rent interval = 6,570.00 + 0.00 = 6,570.00

Units in 40th percentile rent interval needed to reach 40 percent of units = 7,000.00 - 6,570 = 430.00

Additional Units as Proportion of Interval = 430.00 / 5,105 = 0.0842

Dollars Added to Lower Limit of Interval to reach 40th percentile rent = 0.0842 x $250 = $21

**40th percentile standard quality Recent Mover Gross Rent = $1,000 + $21
= $1,021 **

The difference between the actual 2015 ACS Standard Quality Recent Mover Gross Rent of **$1,006**
and the demonstration 2015 ACS Standard Quality Recent Mover Gross Rent of **$1,021** computed here is
due to the effects of rounding on the public distribution as described above.

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