The distributions behind the update factor calculations for Prairie County, MT use the ACS data compiled for the Prairie County, MT. The following distribution demonstrations will be the same for all areas using Prairie County, MT ACS data.
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 2014 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 Montana in 2014 is $334.
The following table and calculations demonstrate how the 40th percentile 2014 ACS standard quality Recent Mover Gross Rent is determined for Montana 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 $334 |
$0 to $300 | 480 | Not in Distribution | Not in Distribution |
| Units in interval containing public housing rent level of $334 |
$301 to $333 | 85.00 | Not in Distribution | Not in Distribution |
| $334 to $349 | 40.00 | 0.3% | 0.3% | |
| Units below interval containing 40th percentile standard quality Recent Mover Gross Rent of $679 |
$350 to $649 | 3,660 | 30.4% | 30.7% |
| Units in interval containing 40th percentile standard quality Recent Mover Gross Rent of $679 |
$650 to $699 | 1,905 | 15.8% | 46.5% |
| Units above interval containing 40th percentile standard quality Recent Mover Gross Rent of $679 |
$700 or more | 6,440 | 53.5% | 100.0% |
| Total Units Above Public Housing Rent in Standard Quality Recent Mover Gross Rent Distribution | 12,045.00 |
The numbers of units with standard quality Recent Mover Gross Rents above and below the Public Housing Rent level of $334 for Montana is determined using linear interpolation over the 125 units in the rent range $301 to $349. Linear interpolation uses the assumption that the 125 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 (125) that have rents below the Public Housing Rent level.
Proportion of rent interval below the Public Housing Rent Level: ($334 - $301) / $49 = 0.6735
Units in the Public Housing Rent Level Interval below the Public Housing Rent Level: 0.6735 x 125 = 84.18
The 40th percentile standard quality Recent Mover Gross Rent for Montana is computed by linear interpolation over the 1,905 units in the rent range $650 to $699. Linear interpolation uses the assumption that the 1,905 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 = .4 x 12,045.00 = 4,818.00
Units below the 40th percentile rent interval = 3,660.00 + 40.00 = 3,700.00
Units in 40th percentile rent interval needed to reach 40 percent of units = 4,818.00 - 3,700 = 1,118.00
Additional Units as Proportion of Interval = 1,118.00 / 1,905 = 0.5869
Dollars Added to Lower Limit of Interval to reach 40th percentile rent = 0.5869 x $50 = $29
40th percentile standard quality Recent Mover Gross Rent = $650 + $29 = $679
The difference between the actual 2014 ACS Standard Quality Recent Mover Gross Rent of $680 and the demonstration 2014 ACS Standard Quality Recent Mover Gross Rent of $679 computed here is due to the effects of rounding on the public distribution as described above.
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