Warm Up
 Bandana Republic
 Populations are as follows:
Apure: 331,000
 Barinas: 267,000
 Caraboro: 133,000
 Dolores: 69,000


Apportion using Webster method with 160 seats.
Hill - Huntington
METHOD CURRENTLY USED
Hill – Huntington
 Method used since 1940 to apportion seats in U.S.
House of Representatives.
 Uses geometric mean

Geometric mean of a and b is the square root of the product of
a and b =
Hill - Huntington
 Rounding Rules
 Use the geometric mean of LQ and UQ: sqrt(LQ*UQ)
 If the standard quota is greater than or equal to the geometric
mean, use the upper quota.
 If the standard quota is less than the geometric mean, use the
lower quota.
 Changes at critical divisor
 If number of seats is too small critical divisor is
 If number of seats is too large critical divisor is
Practice Problem
 The Placerville General Hospital has a nursing staff
of 225 nurses working 4 shifts: A, B, C, and D. The
number of nurses apportioned to each shift is based
on the average number of patients per shift, given in
the following table.
Shift
Average #
of patients
A
B
C
D
871
1029
610
190
Practice Problem
 Steps:
 1. Find the Standard Divisor
Total population ÷ seats
 2700 ÷ 225 = 12


2. Find the Standard Quota for each state (shift)
A: 72.58
 B: 85.75
 C: 50.83
 D: 15.83

Practice Problem

3. Find the geometric mean
A: 72.58
 B: 85.75
 C: 50.83
 D: 15.83


sqrt (72 • 73) = 72. 50
sqrt(85 • 86) = 85.50
sqrt(50 • 51) = 50.50
sqrt(15 • 16) = 15.59
4. Lower quota or upper quota?
A: 73
 B: 86
 C: 51
 D: 16
 Sums to 226.

Practice Problem

5. Will need to use the following critical divisor because there
are too many seats.
A: 12.01
 B: 12.03
 C: 12.08
 D: 12.26
 A loses a seat because it has the smallest critical divisor


6. Final apportionment
A: 72
 B: 86
 C: 51
 D: 16

Practice Problem
 SMART buses have 6 routes (A, B, C, D, E, and F).
They have 130 buses to apportion among the routes.
 Average number of daily passengers






A: 45300
B: 31070
C: 20490
D: 14160
E: 10260
F: 8720
Practice Problem
 1. Find Standard Divisor
 SD = 1000
 Find the Standard Quota for each state.
 A: 45.3
 B: 31.07
 C: 20.49
 D: 14.16
 E: 10.26
 F: 8.72
Practice Problem
 Standard Divisors






A: 45.3
B: 31.07
C: 20.49
D: 14.16
E: 10.26
F: 8.72
 3. Geometric Mean






A: 45.50
B: 31.50
C: 20.49
D: 14.49
E: 10.49
F: 8.49
(use LQ)
(use LQ)
(use UQ)
(use LQ)
(use LQ)
(use UQ)
Practice Problem
 4. Tentative Apportionments
 A: 45
 B: 31
 C: 21
 D: 14
 E: 10
 F: 9
 Adds to 130
 We are done!
Practice Problem
 The Graduate School at Great Eastern University has
15 graduate assistantships to apportion based on the
following enrollments.
 Education: 940, Liberal Arts: 1470; Business: 1600;
For a total of 4010.
 Apportion the seats based on Hill Huntington
method.