142

DISTRIBUTIONAL PATTERN OF SOCIAL GROUPS IN HIGHER

EDUCATION IN INDIA: AN ANALYSIS OF CENSUS DATA, 1991-2001

Introduction

For achievement of higher sustainable growth rates it is very important to introduce a set

of government policies which should include encouragement of higher rates of human

resource development through education. Increase in the percentage of population in the

age group 15-29 combined with a higher demand in higher education with limited

resource does have its impact on the distributional pattern of educational level between

the social groups.

Hence, it becomes important to understand as to how and what are the factors associated

with different social group’s representation in higher education and what are the factors

that controls the growth of population and ultimately the distribution of population in

higher education by social groups. In order to study these significant factors the following

question need to be addressed and examined:

• Does the present level of representation of a social group at a given level of

education have any impact in the future representation and distribution pattern in

higher education by social groups?

• Does the present distribution by age and social groups have any impact on the

future representation in higher education by social groups?

• If Yes, what are the factors that contribute to the accessibility and ultimately the

representation in higher education?

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Keeping this in view, this paper is an effort to understand the influence of fundamental

principles of population growth in higher education and to study the factors affecting it.

Predictive quantitative models derived from the principle of population growth are used

to understand how different social groups interact to attain higher education within

limited resources. This analysis is a humble attempt to understand the functional

prospects of different social groups, and its influence on the corresponding level of

education by building upon the rate of change of individual population of various social

groups in higher education.

For the purpose of linking populations and interactions among different social groups,

such as SC (Scheduled Castes), ST (Scheduled Tribes) and Others caste, we need to first

study the fundamentals of population growth in higher education. Population growth in

higher education is determined by two major factors a) the population in a given age

group deemed to be in higher education, and b) the availability of resources that is the

number of seats available for this given age group in higher education.

The model given below shows the Supply- Demand interaction by social groups and will

simplify the linkage between population for a given age group and resources available.

On the Supply side, is the population at a given age group with completed level of higher

secondary education, and waiting to enroll into further higher level of education provided

there is enough availability of seats or resources. Whereas on the Demand side is the

higher educational system, with different courses designed to meet the growing demand

of technical and higher education in industries and service sectors.

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In the Indian context, with a population in the working age group leading to a surplus

from the supply side which in turn creates constraints in the demand side. In such

situation, the carrying capacity and the competitive factor evolve and determine the

outcomes.

This papter will further explore both these factors in higher educational system in India.

The carrying capacity further would be applicable to both the supply and the demand

side. On the supply side, there are different social groups of India in the age group

between 15-29 years. The population considered should have minimum level of desired

education so as to be eligible into higher educational system which means completion of

at least matriculation level of education to be eligible for higher secondary and so on.

Whereas on the demand side, there is an intake capacity of various education institutes

with a fixed number of seats. In such a situation, there arises the competition factor,

competition within a social group by background characteristics and between the social

groups. Competition between the social groups is the proportion of the population

available with minimum requirement of education from each of the social groups

competing for the same resource (limited number of higher educational seats in

educational institutes).

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The carrying capacity K

This section briefly describes the carrying capacity and how it is used in this analysis.

‘Carrying capacity’ ideally is defined as the number of individuals that can be supported

in a given area within resource limits. It needs to be also noted that it should be without

degrading the natural social, cultural and economic environment for the present and

future generations. The carrying capacity for any given background is not fixed. For our

study, we considered two aspects in achievement of higher education; the first is the

demand side that is the population in a particular age group from different backgrounds

competing to achieve an educational status. The other aspect is the supply side in terms of

availability of education. With a growing population in the age group 15-29 and with

constraints in resources that is the availability of seats the competition for the available

resource is intense. Carrying capacity in this case is the upper limit from the supply side

that is the availability of seats beyond which there cannot be further intake of any

population of that particular age group. However, recently with the improved technology

carrying capacity which we denote as (K) can be altered, but mostly it could be changed

for the worse due to the pressures from demand side accompanied with an increase in

population. As the environment is degraded, K reduces leaving the environment, such

that it no longer supports the number of people, who could formerly have lived in the

area on a sustainable basis. No population can live beyond the environment's carrying

capacity for very long (Hardin, 1977).

Using the above given definition of carrying capacity (K), in this chapter we define

carrying capacity as the maximum supportable population (proportion wise-age wise and

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education wise) existing in a given social group within a limited resource. A minor

change in the carrying capacity (K) will change the growth rate (r) with respect to time.

For example, during a given time period let us consider that there are ‘n’ numbers of

people each being distributed into different social groups say ‘g’. The total ‘n’ number of

population for a given age group and with a minimum level of education is considered

here as a base population. The population considered here is also with minimum

qualification such as to make them eligible or compete for entry into higher level of

education. The total population ‘n’ for each of the social groups changes from one time

period to another as a result of change in the rate of growth ‘r’ of population from one

time period to another time period and simultaneously depending upon the eligibility of

the population (the minimum educational qualification required for entry into higher

education). Hence this supportable population in a given environment is known as the

carrying capacity (K) of the population, belonging to given social groups.

Hence this carrying capacity K will have an impact among different groups of population

if all the groups are at different level of K then it can becomes complex if there is an

interaction between the social groups which is quite evident due to the requirement of

each social group for a common resource. The interaction becomes more prominent when

this homogenous group of population from different social group enters into a given level

of education with a fixed number of seats. The carrying capacity will be an important

factor in their representation and distribution in higher education by social groups. Here

carrying capacity K acts as a strong binding force in the total resource as well as the

proportionate representation of population by different social groups. For the present

study, we consider carrying capacity (K) to be the maximum population available in the

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given age group constrained to the availability of resources, once the population reaches

the level of carrying capacity the growth rate becomes negative over the given time

period.

Let us denote P the population represented at a given level of education, which is lesser

then K (the ideal or actual population). It can be interpreted as the proportionate

population in the given age group, which must reach the educational level K in an ideal

context. Hence the growth rate of the population ‘r’ is given by:

)1(K

Prr o −= (A)

When P < K, consequently r is very high and is approximately equal to ro

and when P > K then the growth rate r becomes negative.

At lower densities, P is very less than K and the population growth rate is high and equals

to ro. However, this is true only when there is an absence of any competition between the

social groups, since the resource is limited, always there is a possibility of competition

between each of these social groups.

In such a case, the present representation of population can be used to assess the future

growth rate by using equation (A) and its implication in the future distribution in the form

of proportional representation at each level of education by different social groups.

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The Model

Let us assume that there are two populations P and Q competing for the same resource for

our analysis, ideally it would be three groups say P, Q and R, representing the caste SC,

ST and Others. Let ri’s be their respective rate of change from time t to time t + n, which

differs by social groups. The rate of change is calculated as given above in equation (A).

Let c.f denote the competition factor between the populations for a limited resource. Let

‘H’ be the limited source which is the total number of population in a given level of

education for the population in the age group 15-29 years. This is the total number of

population considered for higher education. Competition will occur between the same age

group of population competing for the same level of education and the rate of change

between two time periods of the population can be used to model their independent

growth.

If we assume that all the population in the social group are at the lower level of carrying

capacity, then the rate of change will keep increasing or will became high as shown in

equation (A). If any one of the social group has population less than the carrying capacity

K and the other group having value greater then carrying capacity K, then it will lead to a

situation wherein one group is underrepresented and the other group is overrepresented.

Here the group which is overrepresented is the advantageous group in the model. It

would further result in a higher representation in education, which can be determined by

the difference in the proportionate representation of the population for the given age

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group considered and the present proportionate representation at the given level of higher

education that is the resource H.

Hence for )1(K

P− an additional factor will include, which is the differentiable

population between the proportionate population in the given age group, and the

proportionate population represented for a given resource by social group. In the same

age group, if there are more than two populations competing for the same resource say R,

then the differentiable population denoted by d.f of the population which is

overrepresented will be divided between the two population P and N by their weights

denoted by wi.

Then the population at time t+n can be modeled as follows:

The following are the couple of equations of the population which is determined at time

t+n (where n=1, 2,…) :

Pt+n= r1 * Pt * (1- c.fQtRt– w1) …….. (1)

Qt+n= r2 * qt * (1- c.fPtRt– w2) …….. (2)

Rt+n= r2 * rt * (1- c.fPtQt– w3) ……... (3)

Each set of equation for the time period t and social group P, Q, and R with the sub-

indices 1, 2 and 3 are used to indicate the ri(rate in change), wi(weights), and cfi

(competition factor) where i=1,2, and 3 reflects the characteristics of P, Q and R

respectively. For example r1, w1, cf1 reflects the rate in change, weights, and competition

150

factor respectively of population P. The new term in equation (1) c1 Qt (and equivalently

in equation (2) c2 pt) is the one that takes into account the competition factor. As the

population of the other group increases, these new term increases and, as it is been

subtracted by one it slows down the rate of change of group P. Hence it is observed that

the carrying capacity under this scenario depends on the competition factor as well as

weights of the other population and becomes K1 – c1 Qt. A very interesting thing observed

in this set of coupled equations is that the carrying capacity becomes dynamic, instead of

being a constant, the value changes over time.

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Data requirements

This model requires age structure of the population by educational level of different

social groups for two time periods. For the analysis of study in this chapter, we have used

data from Census of India, for two time period 1991 and 2001. Scheduled Castes (SC),

Scheduled Tribes (ST) and Others are recognized as social groups in the study. Census

does not provide data on Other Backward Caste (OBC) and therefore, the others category

include both OBC and Other caste.

The size of the population in the next time period depends, upon the present age structure

of the population. It does not take into account the fact that not all members of the

population will achieve with different types of educational level, and the population for

the next time period is a function of the present population. Hence, for the present study

we consider three age groups 15-19, 20-24, and 25-29 years with educational level

matriculation plus higher secondary and above for the first age group, and, graduation

and above as the completed educational level for the second and third age group

respectively. These age groups along with a given level of education were considered

mainly because majority of the population in the respective age group are with the given

level of higher education.

As it is known that with level of education by different social groups, it is assumed that

with limited resources, all these social groups will be competing for the same resource.

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Calculations

By using equation (1) (2) and (3) we can determine the following factors:

• Distribution of projected population by age group at a given level of education.

• The carrying capacity that is the maximum level of representation in higher

education to which a given group of population will reach with a given level of

minimum education.

• The competing factor in the given age group which will have its effect in the

future distribution pattern by level of education.

Data of educational level in a given age and social group for Census 1991 and 2001 is

used in the analysis of study. Here we use educational level of three age groups 15-19,

20-24 and 25-29, the lower limit is matriculation and above whereas the upper limit is

graduate and above. Hence, it can be assumed that, those in the age group between 15-19

years have at least completed matriculation and higher secondary. Hence the total

education level of matriculation and higher secondary were used for the age group 15-19.

However, in the age group 20-24 and 25-29, years we consider graduate and above as the

minimum level of education, since it is assumed that, the population with higher

secondary would have completed graduation at a minimum age of 20 years. Moreover

age group 20-29 years, reaches its peak and during this period the competition level will

be very high due to limited number of resources.

Table 1 presents the age distribution of population by social groups for the census year

1991 and 2001. Almost in all the social groups, there is decrease in percent representation

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of population with higher education, except for the Other caste. For caste Others, there is

an increase in the percent of population with higher education in all the age groups. In the

estimation of the model, population with higher education in the age group 15-19 years

in 1991 would be 25-29 in 2001. It is assumed that the mortality and migration

component did not change much during that period, and remained more or less same

during the time period across the age groups.

Table 1: Percent and age wise distribution of social groups during 1991-2001.

Social

Groups

15-19 20-24 25-29

1991 2001 1991 2001 1991 2001

SC 10.98 10.48 10.88 9.80 11.77 9.70

ST 8.47 8.52 8.33 7.88 8.81 7.97

Others 80.81 80.98 80.77 82.30 79.41 82.31

Total 100.00 100.00 100.00 100.00 100.00 100.00

Source: c-series socio-cultural tables; Census of India; Registrar general of India, New Delhi, 1991 and

2001.

The ratio of population represented in higher education to the total population in the

given age group by different level of education in a given time period t (base time period)

time and time t+n is estimated. It is considered that the carrying capacity is the total

resource (H) available at the given level of education for a given age group and by social

group and N is the total number of population in the specific age group for a given

educational level. The difference in the value of the estimated and given population is the

differencing factor. For example in the age group 15-19 years, it is assumed that the

majority of population will be those who has achieved the educational level matriculation

and higher secondary and above. The proportion of population of SC, ST and Others with

an educational level of matriculation and higher secondary in the age group 15 -19 years

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to the total number of population in the same age group is calculated to know the value of

P/K. The difference of P/K with the proportionate population of this age group will be

denoted as d.f (the differentiating factor) which will give the difference of the actual

population to the population that should have been there ideally at the given level of

education.

Table 2 presents the value of P/K and Df (differencing factor) in different age groups and

by social groups for the time period 1991 and 2001. For the age group 20-24 and 25-29

years only graduate and above is considered since it is assumed that the highest

educational level achieved in these age groups are graduate and above.

Table 2: Value of P/K and D.F 1991-2001 for different

age groups and by social groups

Social

Groups

P/K D.F

1991 2001 1991 2001

Age Group

15-19

SC 0.087 0.092 0.022 0.011

ST 0.031 0.041 0.053 0.043

Others 0.881 0.865 -0.073 -0.055

20-24

SC 0.039 0.068 0.069 0.029

ST 0.009 0.02 0.073 0.058

Others 0.95 0.911 -0.143 -0.088

25-29

SC 0.033 0.07 0.084 0.026

ST 0.008 0.02 0.079 0.058

Others 0.957 0.908 -0.163 -0.085

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From the value derived for differencing factor in table 5.5.2, it is evident that among

caste SCs and STs, the value of P/K has increased from the period 1991-2001, indicating

that the percentage of population at the given level of education has increased. However,

for caste Others, the value of P/K is approximately close to one and there is hardly any

difference during the decade. Hence, the caste Others have almost achieved the level of

education (or its carrying capacity), whereas caste ST and SC, are still lagging behind as

implied by the value of P/K which clearly indicates that it is too small to be close to one.

In this model, the differentiating factor captures the proportion to be covered. The

proportion gap among the caste SC’s, ST’s is higher especially in the given age group 20-

24 and 25-29 years. The negative value of differentiating factor of the Other caste

indicates that, the actual carrying capacity of the population with respect to the available

resource is more than the required capacity in terms of representation in a given level of

education. Consequently, the population represented by the caste Others estimated by the

differencing factor, when considered in terms of equal representation at each level of

education it has to be represented (added) by the caste SC’s and ST’s for an equitable

distribution by social groups at different level of education.

Rate of change

In this analysis we have also estimated the rate of change in population for a given level

of education and by age group. It is calculated between the two time periods and is given

by (Pt+n-Pt)/Pt. In this model, it is presumed that in future, the rate of change will be

affected by the present competition of the population competing for the same resource,

which has been calculated using equation (1) and (2) by population in different social

groups.

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Table 3 presents the rate of change by social groups and for different age groups. It can

be seen from the table that the rate of change for caste SCs and STs is always higher than

that of the Other caste. This may be due to the fact that, at lower level of representation

the population tends to change or grow at a faster rate rather than, those which are at the

higher level of representation. It may be noted that the population has to reach to its

carrying capacity when N<< K but in addition it also has to compete for resources with

other social groups competing for the same resource.

Table 3: Rate of change during the time period 1991-2001 by educational level and

social groups and age-group

Social

Groups Age Group

15-19 20-24 25-29 R15-19 R20-24 R25-29

SC 1.101 2.047 1.128 ST 1.625 2.647 1.495 Others 0.946 0.682 0.571 Total 0.983 0.755 0.631

As revealed from table 3, the rate of change in educational achievement for caste Other is

lower than that of SC’s and ST’s. However, can we conclude that the lack of

representation of SC’s and ST’s, is due to the overrepresentation of caste Others? If yes

then to what extent caste Other impact the equitable distribution in higher education.

Hence to study the impact of the caste Other representation in the overall distribution of

higher educational by social groups, we find the difference between the proportionate age

group population with caste ST and SC and the proportionate population in that

educational level which will be c.f (competing factor) and then this competing factor to

the total competing factor of Others which will be the respective weights. That is the

extent to which the competing factor of caste Others will influence on the rate of the

change between the two decades.

157

Then, using the competing factor and the weights calculated, the new rates are estimated

by using equation (1), (2) and (3) and r1* (1- c.fqt– w1) is estimated for different

populations.

Let us denote the terms:

(1- c.fqt– w1) = f and r1* (1- c.fqt– w1) = r’.

Since the value of d.f (differencing factor) was negative for caste Others, we assume that

caste Others has already reached the carrying capacity in terms of achievement in higher

education. Since the negative value implies representation in higher education is

exceeding the available resource, the c.f (competition factor) will be nil in such a case

and hence the equation reduces to (1- w1) only for caste Others. The c.f factor in this case

will affect the rate of change, such that even though if caste SC’s and ST’s which has not

yet reached the carrying capacity K. The rate of change of these groups will not be as

high as required for them to reach the carrying capacity ideally. The new rate of growth

‘r’ is the rate of growth after taking into account the value of (carrying capacity) K and

(competing factor) c.f by social groups.

Table 4: Value of competition factor (f ) and rate of growth (r’) for the period 1991-

2001 by different age social groups

Social Groups f r’

Age Group

15-19

SC 0.772 0.85 ST 0.172 1.279 Others 0.944 0.894

20-24

SC 0.632 1.295 ST 0.279 1.741 Others 0.911 0.622

25-29 SC 0.66 2.226 ST 0.253 1.018 Others 0.914 0.914

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Table 4 presents the competing factor, weights and the rates calculated for different social

and age group. Higher growth of rate indicates that, the given population requires a larger

percent of population at a given level of education in a given age group. However, due to

the influence of the competing factor (f), the value of growth rate r’ changes

considerably.

The lower the value of competition factor f, the higher is the value of ‘r’, which implies

that there is an inverse relationship between them. From the values calculated in the table

above, it is evident caste SCs and STs requires a higher rate of growth r’ as compared to

the Other caste. Again the rate of the growth is higher in the age group 20-24 and 25-29

years compared with 15-19 age group indicating that at higher level of education the

required growth rate is higher to reach at the required capacity for the respective social

groups.

Table 5 presents the expected distribution in higher education of the population if the

competing factor factor f is applied. To get the expected population in the next decade,

the simple rate of growth is estimated from census 1991 and 2001; and the average

growth rate is used to estimate 2011 population. After estimating the population, the

percent wise distribution of the population is given below.

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Table 5: Projected percent wise distribution in 2011 by educational

level of social and age group

Social Groups 1991 2001 2011 (projected)

Age group

15-19

SC 8.77 9.29 9.14

ST 3.16 4.18 3.35

Others 88.18 86.52 87.51

20-24

SC 3.93 6.82 11.18

ST 0.9 2.04 2.22

Others 95.08 91.12 86.66

25-29

SC 11.77 9.7 8.69

ST 8.81 7.97 9.28

Others 79.41 82.31 82.03

Total 100 100 100

Table 5 presents the distributional pattern by different social groups and age groups, the

fourth column being the calculated distribution pattern for the year 2011. For the age

group 15-19 years, it is expected that the competing factor f will further lower the

representation of caste SCs and STs distribution in given educational level when

compared with Others caste. However, in caste Others the percentage of population in the

distribution has increased. The distribution shows the decrease in the percent

representation of caste SCs and STs. This indicates that although the rate of change

might be higher, the competing factor decreases the rate of change in the future

distribution. Hence, the competition factor f will have an impact on the distribution

pattern and play an important role of the future population by educational level for

different age groups.

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Table 6 Percent wise distribution by educational level

of social groups and age-groups

Social

Groups

1991 2001 2011 (expected)

Age group

15-19

SC 8.77 9.29 9.22

ST 3.16 4.18 2.87

Others 88.18 86.52 87.9

20-24

SC 3.93 6.82 9.37

ST 0.9 2.04 2.13

Others 95.08 91.12 88.49

25-29

SC 11.77 9.7 11.28

ST 8.81 7.97 2.1

Others 79.41 82.31 86.6

Total 100 100 100

Table 6 presents the percent wise distribution of the population without the competing

factor and the estimated new growth rate. In all the age groups excluding caste SC and

ST population, the caste Other percentage of population with higher education has

increased.

Table 7 presents the overall estimated percent wise distribution of population with and

without competing factors. In the age group 15-19, without the competing factor, there is

a considerable difference in the percent wise distribution of the population. This

difference is due to the growth rates though marginal but although are evident.

Comparatively, in the age group 20-24 and 25-29 years, the gap widens in terms of

achievement in higher education between the caste SC/ST and caste Others with higher

percent of population in caste Others. The difference in the distribution is due to the

growth rate as well as that due to the competing factor.

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Table 7: Expected percent wise distribution in 2011 by educational level of social

groups and age-group with and without competing factor

Social

groups

1991 2001 2011

(expected)

2011 (with

only r’)

2011

(without c.f)

Age group

15-19

SC 8.77 9.29 9.22 9.73 10.25

ST 3.16 4.18 2.87 5.47 6.81

Others 88.18 86.52 87.9 84.79 82.92

20-24

SC 3.93 6.82 9.37 11.07 11.78

ST 0.9 2.04 2.13 4.06 5.02

Others 95.08 91.12 88.49 84.85 83.2

25-29

SC 11.77 9.7 11.28 12.23 12.98

ST 8.81 7.97 2.1 2.99 3.06

Others 79.41 82.31 86.6 84.78 83.96

Total 100 100 100 100 100

Drawback of the Model

Although the model can be used to estimate the future distribution pattern by educational

level and social groups, there are other factors which might also influence the rate of

change such as preference of education, employment and gap in achievement of

educational level. For the present study, it was assumed that the above trend might not

have changed during a short interval of time, hence it can be said that the expected

distributional pattern can be used for only a short period of time. It is also assumed that

the mortality and the migration during the time period and also between the social groups

remains more or less same which may or may not be true.

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The main objective of this papter was to explore the influence of simple growth rate and

the competition factor influencing the future distribution in the representation of

population ie the representation of population distributed by age and social groups with

completed level of higher education.

The results reveals that if we use the average growth rate of past two census in estimating

the future distribution of population in higher education by social group, the

distributional pattern remained more or less same. Whereas, if we consider the growth

rate taken into consideration the effect of carrying capacity of the population, the

distribution pattern more or less remains same, but the gap widens between the caste SCs

and STs with Others caste affecting the distribution pattern in terms of achievement in

higher education.

However, with the application of the competing factor it was evident that the gap among

the social groups further widened leading to a skewed distribution of population by social

groups in higher education with larger percent of population concentrated in the Other

caste. It was found that there is a considerable decrease in the percent of the population of

caste STs and SCs. However, due to the effect of the competing factor, there is an

increase in the percent population of the Other caste, thus negating the influence of

change in growth rate.

Therefore, it can be concluded that when we project the distribution of the population, we

cannot exclude the influence of competitive factor between the social groups in terms of

163

achievement in higher education. The competitive factor in terms of distribution of seats

in higher education by social groups along with the influence of carrying capacity does

have an influence on the distribution pattern of the population in terms of achievement in

higher education hence cannot be ignored. To project the future growth rate of the

population may give only a vague picture if only the average growth rates are considered.

The growth rate therefore should ideally take into consideration the rate of growth rate of

the Others caste population having a larger representation in higher education when

comparing with ST and SC, since all are competing for the same resource. Analysis

revealed the differences in distribution of higher education by age group and social

groups. However, the difference in distribution is more evident in the age group 20-24

and 25-29 than in the age group 15-19. By implication, the difference is much more

evident in the higher age groups than in the lower age group and comparatively at higher

level of education.

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