HomeMy WebLinkAbout1975-05-29-SLRE-rpt.pdf REPORT OF THE LEXINGTON SCHOOL COMMITTEE
SUBCOMMITTEE ON LONG-RANGE ENROLLMENT
29 May 1975
Jack H. Monderer
Eric T. Clarke
In 1974 the Lexington School Committee appointed a subcommittee. to provide
it with near-term enrollment projections for the Lexington public schools. In carrying
out this task the subcomtnittee used the cohort survival method for projecting the most
probable number of children that would be enrolled in each class in each year. Each
number was obtained by multiplying the number of children in the immediately lower
grade in the previous year by the average percentage change that had been experienced
in that grade transition during the previous five years. This method has been shown to
be fairly dependable for projections extending for about ten years. However, because
it depends on knowing the initial size of each cohort at birth, the method is in principle
unable to project a given class size further into the future than the average age of the
children in it. In practice, it turned out that the cohort survival. method could safely
be applied only as far as 1978 for elementary grades and as far as 1983 for secondary
grades.
Early in 1975 the School Committee, faced with the need for decisions with respect
to school building utilization and modernization, appointed a second subcommittee to
investigate whether any sort of enrollment projections for the years between 1980 and
2000 could be made. After some deliberation, the subcommittee agreed that the most
productive approach would be to assume that Lexington is basically a small sample of
the U. S. population, somewhat modified by local social-cultural patterns, that is con-
tinually refreshed by In-migration and therefore continues to be representative. If this
assumption were tested and found to be essentially correct, then the subcommittee could
use national school enrollment projections, suitably adjusted to fit local conditions, to
arrive at credible predictions of Lexington school enrollments over the same period of
time.
National school enrollment projections are prepared from time to time by the
U.S. Office of Education, working with census figures and the expressed expectations
of American mothers as determined in numerous census surveys. The projections are
based on specific assumptions about completed fertility rates, i.e. , the total number
of children to be expected per family. Until a few years ago, projections showed
•
2. .
rapidly increasing enrollments at all grade levels, but in Bpite of the continuing rise
in overall population they are now decreasing because of sharply decreasing fertility
rates that first became evident about fifteen years ago. Today, national school enroll-
ment projections center around two assumed expectations of completed cohort fertility
rates, Series E (2.1 births per woman) and Series I" (1. 8 births per woman), because
recent experience will support no higher levels. (1974 total fertility rate was 1. 862
births per woman, compared to the maximum of 3.760 in 1957. )
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Fig 1 shows the resulting steady decrease in elementary school population in the
1970 decade followed by either a gradual increase or a period of stability depending
on which fertility rate is assumed. Secondary school population repeats the trends
shown for elementary schools but with delays of about six years. Such projections
can be used to estimate Lexington° s probable future enrollments if the relationship
between the Lexington and the US population can be established.
3,
To determine this relationship, the subcommittee agreed to investigate whether
population age distribution and age-specific fertility were useful measures of the degree
to which Lexington' s population could be considered a sample of the national population.
If it could be concluded that Lexington' s future enrollment trends were likely to follow
the national pattern, then it would be a simple matter to adjust the national figures to
take into account purely local factors, such as Lexington' e expected overall growth
rate as measured by the total number of families, and the relative fertility of Lexington
women compared to the national average.
U.S. census data for 1950, 1960 and 1970 give the populations of Lexington and
of the U.S. as a whole in five-year age groups. The census publication, "Population
Characteristics" provided Lexington data for the respective years; national statistics
were obtained from the 1973 edition of the Bureau of Census publication, "Statistical
Abstract of the U.S. ," reproduced here as Fig 2,
lit!ATINI ATM"! too P110.1 C" to POPULATION, ny Aa m AND SPIX: 1950 TO 2000
,n thousnnds.
As
of July 1,Includes Armed Forces abroad.Projections ea)COI1Ski ent wIth tho April 1,1070 emus,These proYentions were proposed using Ohs"cohort-eon:1)300one"
EI:)1!“10 end njql MO a sliMit Improvement In mortality,en annual net immigration of 400,000,and n completed cohort fertility rata(I,o.,too tworoge numbs of births per 1.000
. .nnen upon comp1et1on of.childbearin) that vial move gradually toward the following I ovels: Series C-2,800;Series D-2,100;Oerlos E-2,10U:Suries 1?-1,900,Sea p.1 for derive-
of estimates and proJectious/
---.. , -...--- - , „....... ........------................---------
,:rAn.51,111EF,AND Total, Under 5, 5-0 10-11 1 15-19 20-24 25-20 1 30-34 35-30 40-44 1 4,5-54 5544 65774 i,75 years, modiari
SEX ell 114,.'S - year i years years 1 wears years years 1 years years years }ears y,..5..4 (ars I and oval hp
'";,0.........,......- t52,271 13,410 13,370 11,233 10075 11,0S0 32,3132 11,074 11,347 10,200 37.453 13,334 8,403 3,003 30.2
00,........„....,. 150,071 20,337 10512 10 923 I 13,455 11,124 10,1:39 11,079 1213,2 11,(10 20,573 15.027 11,055 5,et • 2','.1.
.i
0 20t,R79 r 17,167 19,585 :10,SW I 19,301 1,,1.12 13,1,S1 11,570 11,174 11,L1S2 II,'287 1 ,t0! 12,41.1 ‘,605 220
.,`,"2 '.?;):;,h3;,' -17.2.12 15,702 70,104 I 1:1 101 IA,210 , 10,045 12,300 11,125 11,045 23,091 131,104 12,515 5.101 , 21.1
;crL'ent of total:
1333 181 0 1141 8.8 7,4 7,30 7.7 5,3 1.7 7,6 (J,8 11.3 8.31 06 '20 CO
3130011,3 313.4 13.1 7.4 02 01 0,34 0.31 . (3,13 33,4 8.31 6.3 3.1 tx
10)1.0 8.4 31.1 311.2 31,4 0.4 6.7 00 6.6 0,5 11,4 11.1 , 0.1 3.5 1X3
5.3 13.0) 10.0 0.0 31.7 7.2 1.0 03 00 II,3 31.0 07 011 oc)
2113,3713 110,710
D 21A 321 ig.1G2 • 17,310 20,062 20,013 10.404 17,312 13,802 11„CH 11.117 23,503 10 807 13,540 8 621
1.:„.......... 213025' 10 71;3 ' 2e,tS
le 1333,375 10,210 138.1
Al,13.1,5 1 Fl,110 10,047 28.7
D......,.,.„ G 21,716 18.301 , „ „ ' - - ,... s ...630 „In
13,2, 1 ,r107, • 17,4J,. ..C1.221 -I,007 10,544 1,,413 13,0.2 11,548 22,400 -/,083 /i
"'
1:. 13:11,435 16,827 10,70:3 .1, 213.8
1030-C...... 230,73'3 27,1-131 70,803 23,715 10,104
1.1...,... 25s,02 173,305 21,310 72,021 /5,650 .1 21 5
'1 .,;8,G39 20,331 20,704 15,5S5 17,262 1 17,523 20,601 21,290 10013 37,"07 21,017 g0,357 18,70 30,J31
1, 1.3',1,01 37,7513 35,254 17,154 10.710 i .t M.
1
1,4r)2---(.1.„„,,., 300 400 1 20,400 21,51,0 27.440 2:7,ro 24.23. 10.310 ' ' 213.1
V3 43
AG 23,5,nt 24,819 GI 0 2-1,72A 12,.. , 15,0.,. IS,110 20,230 ' 21103 35,720 22,tas la,'..,71. 12,An 31-1
E , 51 1../,152 11 C94 20, 21,018 10,210 17,502 '
F---•••-•-•• 250.6'40 13 15,1102 111,514 35,0133. 1331,3.136 17,40') I 17,002 1 i1 t3, 33136
To reduce these figures to average population per family, the Lexington data for each
of the three years were divided by the corresponding number of assessed dwellings plus
apartment units as determined by the Lexington Board of Assessors. The U. S. data
were correspondingly divided by the number of heads of families for each of the three
4
years as reported by the U.S. census. The ratios of the Lexington population per
dwelling and the U.S. population per family were then calculated and plotted in Fig 3.
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The extent to which these ratios approach unity Indicates the degree of representa-
tiveness of Lexington' a population relative to the U.S.
The most dramatic aspect of Fig 3 is the deep notch indicating the relative
scarcity of members in the Lexington population between the ages of 20 and 30, As
the youthful population reaches adulthood, it leaves town. Not until they reach their
late 20s do younger people come to Lexington, presumably when they have established
themselves sufficiently to be able to afford the housing relinquished by retiring couples
whose children have grown up and departed. *
*Appendix A shows the age distributions of adult in-migration and
of the 1970 population.
. 5.
When they do move into Lexington they of course bring with them their young children,
whose earlier absence is indicated by the relative scarcity of preschool (0-4 age)
children in the Lexington population distribution. Fig 3 indicates that the Lexington
population between ages 30 and 60 years and between ages 5 and 17 years is similar
to the national population between these ages, and consequently that national popu-
lation projections may be applied to Lexington for enrollment purposes as long as due
allowance is made for the expected capacity of the town.
As a backup to this conclusion, an attempt was made to compare the age-specific
fertility of Lexington women with that of their sisters in the general U. S. population.
For this purpose, data on Lexington births were obtained from the Town Clerk' s records*
for the period 1950 to 1975 and national birth rate information was extracted from the
most recent issue of the U.S. Census publication, "Population Estimates and Projections."
To obtain the Lexington birth rate from the raw birth data, the Lexington female popular
tion: age distributions were drawn from the pertinent U. S. and State census reports. •
Fig 4 tabulates this information and presents the resulting ratios of the Lexington to
U.S. birth rate ,
Fig 4 Birth Rates per 1000 Women, by Age of Mother
Year I 15-19 20-24 25-29 30-34 35-39 40-44 1 25-39
...._-; -e- - ......- -__
a T US aver41:e
1950 79 193 165 101 52 14 ! 91
1900 91 257 197 112 57 15 ' 118
1965 73 194 161 95 46 13 ; 99
1970 69 163 138 72 33 9 85
1975 50 130 110 56 24 6 69
b. LexiWon
1950 12 132 189 151 46 18 i 124
1960 15 203 245 142 69 26 I 135
1965 7 105 214 136 56 7 117
1970 6 0 49 192 98 40 8 98
1975 1 27 11.0 85 16 2 59
,c4.....I.t/Ast2TefUS ratios
1950 .15 .68 1.15 1. 50 . 88 1.3 1 36
, •
1960 . 16 .79 1. 24 1. 27 1. 21 1.7
1 1,14
1965 . 10 . 54 1.33 1.43 1. 22 . 5 / 1.18
1970 . 09 .30 1.39 1.36 1. 21 .9 I 1, 15
1975 .02 . 21 1. 00 1. 52 .67 .30. 85
/
1974 and 1975 data are estimated.
Sources° US Census Report P25 No. 493 - Population Estimates and Projections (1972)
US Census Reports - General Population Characteristics
Lexington Town Clerk' a records
*See Appendix B
6.
The Lexington- US ratios ,of birth rates in the 25-39 age category suggests con-
sistency of Lexington births with national figures, and that the fertility of Lexington
women has in the past been at least 10% higher than the national average but is now
decreasing. The younger age groups are less fertile, but this is undoubtedly because
many Lexington women in these age brackets have not yet left their parents and are
as yet unmarried.
Accordingly, the US data in Fig 2 were used to compute the school age (K-1 2)
population per family for the years between 1950 and 2000. The numbers for past
years (1950-1975) were then compared with the actual Lexington enrollments per
dwelling for the same period; as may be seen in Fig 5 by comparing the US and
Lexington columns for K-12 children, Lexington enrollments per dwellings were
3% greater than the US children per family in 1950 and 1960 and about 8% greater
in 1970 and 1975.
Fig 5 US and Lexington Children per Family and Lexington School Enrollments
US population Lexington Schools
Heads of 1 Children per family in age groups K-12 per
Year Families ' 0-4 5-9 10-14 15-19 K-12 Dwelling K- 12
1950 39.3 ; .42
f
.34 . 29 . 27 .79 . 82 3135
1960 45. 1 1: .45 .42' .37 .30 .97 1,00 6880
1970 l 51. 2 .33 .39 .41 . 38 1, 03 1.11 9460
1975 L 55,530____,31 36 38 . 90 __. 97 8400
19r80--- - 60,4 : .31 . 28 . 29 .33 .77 . 85 7550
E 1.990
1
67.3 q .30 .31 . 28 . 26 .74 . 81 76 20
200t 0 _ . L .. .. Le..26____ ...27 . _ ,29
_, 29 _ ..a73 _ _ 80 _ 7 890
. 27 . 29 .33 .76 .84 7460
F { 1980 60.4 1 . 28 1990 67.3 t . 26 . 27 . 26 . 25 .67 .74 6930
Notes
,
a. Heads of families = actual for 1950, 1960, 1970; thereafter according
to (1/2)(20-65 ages)x.952; this gives 1950=42. 0, 1960=45.1, 197051, 2
b. School children (K-12) estimated from (5- 9) + (10-14) + 0.6 (15- 19)
c. Projected populations based on US Census Series E and F projections
(2.1 and 1. 8 children per woman)
d, Lexington figures;
1950, 1960 - kindergarten added equal to let grade
1980- 2000 projections assumed 10% greater than US average
e. Dwellings; 1950=3815, 1960-6860, 1970-8481, 1975=8676
increasing 5% per decade thereafter.
7.
The more recent figures are consistent with the conclusion that Lexington families
are about 10% more prolific than the U.S. average, and 50 a fertility factor of 1. 1
was applied to the projected number of U. S. school children per family to obtain the
expected Lexington school children per family for the years 1980- 2000. Finally, to
obtain the enrollment projections these were multiplied by the expected number of
dwellings in Lexington during the next 25 years based on the assumption that this
number will continue to increase at its present construction rate of about 50 dwelling
units per year, or about 5% per decade. Rig 5 includes two sets of enrollment pro-
jections depending upon which completed fertility rate (2. 1 or 1. 8 children per family)
is assumed.
By the same process, enrollment projections for Lexington elementary (K-6)
and secondary (7-12) schools were also calculated. For this purpose, the children
in grades K-6 were considered to consist of the 5- 9 age group plus 40% of the 10- 14
60
age group, while those in grades 7- 12 were taken to be Affi% each of the 10- 14 and
15- 19 age groups. Results are shown in Fig 6.
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For comparison purposes, the projection technique was applied to the U.S. data in
- to calculate the expected enrollments for grades 1-6 in 1950 and 1960,
f
8.
K-6 in 1970 and 1975, and 7 -12 in all four years. Fig 6 shows these results,
together with the actual enrollments to indicate the extent to which the projection
method may be depended upon.
The assumed 5% rate of growth of the town is based on the fact that, as shown
in Fig 7, Lexington is apparently approaching its ultimate size.
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.' 111 -0 Pr‘o, if7) rN Kilo 2.000
Historically, families with school-age children live in single-family housing, which
has been constructed at an average rate of 50 units per year for the past five years.
Only a relatively few scattered building lots remain available for future construction,
and costs are high enough to keep the construction rate down to these levels. Future
development of any appreciable magnitude is likely to be devoted to multiple housing,
which historically has been occupied almost entirely by couples whose children have
flown the nest or by young families with preschool children who move into existing
single-family housing as the children reach school age. In any event, Town Meeting
has resisted this type of expansion (only two multiple housing projects have been
approved in the last ten years).
9.
The conclusions of this report rest on three basic assumptions: a) national
fertility rates will continue to trend toward a completed rate of about two children
per family; b) the character of Lexingtons population will remain primarily pro-
fessional and relatively affluent, but its fertility will continue to be generally
representative of the US population; and c) the town will continue to grow slowly
toward maturity at a level of perhaps 38, 000 total population by the year 2000.
The conclusions are as follows:
1) The prediction method developed here is reasonably successful in repro-
ducing enrollments that actually took place between 1950 and 1975;
2) The method predicts enrollments for the next 25 years that are neither
higher nor much lower than 1975 levels;
3) Predictions indicate that after 1980 enrollment levels will not continue to
decline at rates characteristic of the 1970 decade, but will tend to remain relatively
constant over the 20 years from 1980 to 2000,
Appendix A. Lexington Population and Adult
Migration Age Distributions.
The accompanying graph shows the relationship between the resident
population in 1970 and the adult migration into Lexington for the years 1959,
1964, and 1973 The population total was taken from US Census sources and
the in-migration data were drawn from the Lexington residential listings for
the three years and thus do not include minor children. It may be seen that
the annual in-migration represents about 10% of the adult population and peaks
at about age 30.
This process of in-migration of young families (which is to some extent
balanced by out-migration because of employment changes) has thus been going
on for at least a decade and seems unlikely to change in the future. As shown
viE P-Jeri/dr-,
in FtnEEF , it has never been sufficient to make up for the loss of Lexington' s
young people. However, it serves to maintain an equilibrium distribution of
adult ages, balancing the natural aging of the resident group by a constant
flow of younger adults.
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Appendix B. Births to Lexington Mothers ,-
.._,2dr... 2h._Mothers 25--$9
Year 15-1.9 20-24 25-29 30-34 35-39 41-44 15-44 Women Births.
1950 6 62 115 100 33 12 329 1994 248
1960 12 75 168 157 88 29 529 3058 413
61 10 78 161 143 95 19 506 399
62 13 71 136 141 78 23 463 355
63 7 71 129 142 91 13 453 362
64 12 71 131 122 67 20 425 320
1965 9 68 131 139 73 10 430'2941 343
66 11 87 114 106 60 7 387 280
67 10 64 147 108 46 13 389 301
68 6 56 135 96 42 9 344 273
69 7 56 131 102 40 .11 350 273
1970 9 32 137 97 46 10 331 2844 280
71 7 34 108 79 28 7 263 215
72 4 20 116 68 15 6 230 199
73 3 18 98 85 24 3 231 207
74 1 19 76 85 18 3 202 179
1975 (est) 170 3010 160
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