The following information provides details on how the 2010 **1-Bedroom** ACS 5-Year Adjusted Standard Quality 40th Percentile Rent of
**$434** was developed for Manistee County, MI using the publically releasable distributions from the 2010 ACS.

The standard quality 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 2010 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 **Manistee County, MI** in 2010 is $261.

The following table and calculations demonstrate how the 40th percentile 2010 ACS
standard quality rent is determined for **Manistee County, MI**
using the public distribution of standard quality rents.

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

Units below interval containing public housing rent level of $261 |
$0 to $250 | 130 | Not in Distribution | Not in Distribution |

Units in interval containing public housing rent level of $261 |
$251 to $260 | 0.88 | Not in Distribution | Not in Distribution |

$261 to $299 | 3.12 | 1.1% | 1.1% | |

Units below interval containing 40th percentile standard quality rent of $433 |
$300 to $399 | 85 | 29.6% | 30.7% |

Units in interval containing 40th percentile standard quality rent of $433 |
$400 to $449 | 40 | 13.9% | 44.6% |

Units above interval containing 40th percentile standard quality rent of $433 |
$450 or more | 159 | 55.4% | 100.0% |

Total Units Above Public Housing Rent in Standard Quality Rent Distribution | 287.12 |

The numbers of units with standard quality rents above and below the Public Housing Rent level of $261 for Manistee County, MI is determined using linear interpolation over the 4 units in the rent range $251 to $299. Linear interpolation uses the assupmtion that the 4 units' rents are uniformly distributed in the rent range around the Public Housing Rent level. Under this assumption, the proportion of the rent interval ($49) that is below the Public Housing Rent level is the same as the proportion of units with rents in the interval (4) that have rents below the Public Housing Rent level.

Proportion of rent interval below the Public Housing Rent Level: ($261 - $251) / $49 = 0.2041

Units in the Public Housing Rent Level Interval below the Public Housing Rent Level: 0.2041 x 4 = 0.82

The 40th percentile standard quality rent for **Manistee County, MI** is computed by linear
interpolation over the 40 units in the rent range
$400 to $449. Linear interpolation
uses the assupmtion that the 40 units' rents are uniformly distributed
in the rent range around the 40th percentile.
Under this assumption, the proportion of the rent interval ($50)
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 = 0.4 x 287.12 = 114.85

Units below the 40th percentile rent interval = 85.00 + 3.12 = 88.12

Units in 40th percentile rent interval needed to reach 40 percent of units = 114.85 - 88 = 26.73

Additional Units as Proportion of Interval = 26.73 / 40 = 0.6682

Dollars Added to Lower Limit of Interval to reach 40th percentile rent = 0.6682 x $50 = $34

**40th percentile standard quality rent = $400 + $33
= $433 **

The difference between the actual 2010 ACS Standard Quality Rent of **$434**
and the demonstration 2010 ACS Standard Quality Rent of **$433** computed here is
due to the effects of rounding on the public distribution as described above.

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