The following information provides details on how the 2007 ACS Standard Quality 50th Percentile Rent of $727 was developed for Mifflin County, PA using the publically releasable distributions from the 2007 ACS.
The distributions behind the update factor calculations for Mifflin County, PA use the ACS data compiled for Pennsylvania. The following distribution demonstrations will be the same for all areas using Pennsylvania ACS data.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.
HUD uses rents for standard quality units to generate update factors. "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. built before 1999
f. meals not included in rent
The 2007 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 Mifflin County, PA in 2007 is $257.
Note: For a discussion of the derivation of the cut-off rent, please review the following document: Public Housing Adjustments for FMRsA Microsoft Excel file containing the unsummarized versions of the publicly releasable standard quality 2-bedroom rent distributions for Mifflin County, PA is available here.
The following table and calculations demonstrate how the 50th percentile 2007 ACS standard quality rent is determined for Mifflin County, PA 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 $257 |
$0 to $249 | 16,455 | Not in Distribution | Not in Distribution |
| Units in interval containing public housing rent level of $257 |
$250 to $256 | 686.00 | Not in Distribution | Not in Distribution |
| $257 to $274 | 1,764.00 | 0.4% | 0.4% | |
| Units below interval containing 50th percentile standard quality rent of $727 |
$275 to $724 | 224,425 | 49.4% | 49.7% |
| Units in interval containing 50th percentile standard quality rent of $727 |
$725 to $749 | 15,205 | 3.3% | 53.1% |
| Units above interval containing 50th percentile standard quality rent of $727 |
$750 or more | 213,330 | 46.9% | 100.0% |
| Total Units Above Public Housing Rent in Standard Quality Rent Distribution | 454,724.00 |
The numbers of units with standard quality rents above and below the Public Housing Rent level of $257 for Mifflin County, PA is determined using linear interpolation over the 2,450 units in the rent range $250 to $274. Linear interpolation uses the assupmtion that the 2,450 units' rents are uniformly distributed in the rent range around the Public Housing Rent level. Under this assumption, the proportion of the rent interval ($25) that is below the Public Housing Rent level is the same as the proportion of units with rents in the interval (2,450) that have rents below the Public Housing Rent level.
Proportion of rent interval below the Public Housing Rent Level: ($257 - $250) / $25 = 0.2800
Units in the Public Housing Rent Level Interval below the Public Housing Rent Level: 0.2800 x 2,450 = 686.00
The 50th percentile standard quality rent for Mifflin County, PA is computed by linear interpolation over the 15,205 units in the rent range $725 to $749. Linear interpolation uses the assupmtion that the 15,205 units' rents are uniformly distributed in the rent range around the 50th percentile. Under this assumption, the proportion of the rent interval ($25) that needs to be added to the lower limit of the interval to reach the 50th 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 50 percent of units in the distribution.
50 percent of units = .5 x 454,724.00 = 227,362.00
Units below the 50th percentile rent interval = 224,425.00 + 1,764.00 = 226,189.00
Units in 50th percentile rent interval needed to reach 50 percent of units = 227,362.00 - 226,189 = 1,173.00
Additional Units as Proportion of Interval = 1,173.00 / 15,205 = 0.0771
Dollars Added to Lower Limit of Interval to reach 50th percentile rent = 0.0771 x $25 = $2
50th percentile standard quality rent = $725 + $2 = $727
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