World Applied Sciences Journal 33 (2): 213-219, 2015 ISSN 1818-4952 © IDOSI Publications, 2015 DOI: 10.5829/idosi.wasj.2015.33.02.1

Application of Discriminant Analysis to Predict The Institute’s Annual Performance in Board

12Humera Razzak, Mehboob Ali and 3 Maqsood Ali

1Ex-Lecturer, Department of Statistics, Government College University Faisalabad, 2Government Post Graduate College, District , Pakistan 3Punjab Bureau of Statistics, Lahore, Pakistan

Abstract: This study has been carried out on the annual performance of 2nd Year (12th year education) results 2014 of various institutes affiliated with Sargodha board. Discriminant analysis has been used for achieving sharper discrimination between two categories (group 1: institutes having annual results below board average result and group 2: institutes having annual results above board average result) based on disciplines of institutes, gender, status of institutes and geographical area of four districts in Sargodha division. Successful discrimination is made between institutes with results below or above board average. Clustering annual results of institutes under two categories is statistically significant on the basis of discriminant analysis. The data is obtained from managing body of Sargodha board. Analyzing set of seven variables shows five of them significantly help in discriminating between institutes with result below or above board average. Therefore it is suggested to reclassified institutes who were misclassified under results below board average result.

Key words: Discriminant analysis Sargodha board Institute annual performance

INTRODUCTION into account of individual discipline performance and some other factors that may be more likely to affect its College enrollments have grown rapidly in result. recent years. Concerns about annual performance of The Board of Intermediate & Secondary Education institutes as compared to board results are (BISE) Sargodha was established in 1968 under the West widespread.Since institute annual result rate may not only Pakistan BISE Multan and Sargodha Ordinance. This is 2nd influence student outcome but also effect admission in Punjab in terms of its establishment. At this time process and individual interest toward getting higher Sargodha board authorizes Sargodha, Khushab, education [1]. Practically it is very important to predict and districts [3] BISE Sargodha has the authority institutes success with the help of some set of to organize the exams of matric and intermediate. independent variables including gender and some In this research Sargodha board 2nd year results demographical outcomes [2] in order to seek answer to a 2014 has been predicted under two categories institutes question that what was performance of an institute as having annual results below board average result and compared to board annual result? institutes having annual results above board average Prediction about institute success rate in terms of result based on disciplines of institutes, gender, status of whether its annual result is below or above board average institutes and geographical area of four districts. result is actually a process of determining that which Out of total 230 institutes affiliated with group that particular institute belongs. Typically an Sargodha board the annual results of 93 institutes are institute is declared as having result below or above included, other institutes were dropped from the analysis board average result on basis of overall averages of due to unavailability of all four disciplines in these various disciplines percentage scores regardless of taking institutes.

Corresponding Author: Humera Razzak, Department of Statistics, Government College University Faisalabad, Pakistan.

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Will an institute is more likely to show result above Sargodha board average result 2014 is 60.88. Two groups board average result due to higher performance in General of dependent variable are made on the basis of board Science group? Demographical characteristics of annual average result. The independent variables are institutes have likelihood to effect institute results as Medical students passed percentage of an institute (X1 ), compared to board average results? Reliable answers to Non-medical students passed percentage of an institute all questions related to problem mentioned above are (X2 ), General Science students passed percentage of an seeked in this research using traditionally discriminant institute (X3 ), Arts students passed percentage of an analysis. institute (X45 ), Gender (X ), Status of institution as public

Discriminant analysis is a multivariate statistical and private (X6 ) and Geographical area of four district of technique used in statistics. This technique classifies an Sargodha division which consists on Sargodha, object into one among several groups based on its Khushab, Mianwal and Bhakkar districts (X7 ). The attributes. Discriminant analysis has three main sample/data consists of 93 institutes those have these objectives. First, to identify the attributes that variables and other institutes were dropped from the discriminates among the groups. The second objective is analysis due to unavailability of all four disciplines in to use the identified variables to develop some functions, these institutes. called the discriminant functions, for computing some new Discriminant Analysis finds a set of prediction variables or indices that will parsimoniously represent the equations based on independent variables that are used differences among the groups. The third objective is to to classify individuals into groups [16,17]. In many ways, use the computed scores to develop a rule to classify discriminant analysis parallels multiple regression future observations into one of the several groups analysis. This method formulates linear equation which [4].Classification of various predictive variables has been has been the most recognizable and the simplest already done in many past studies [5-10]. interpretable measure of effect [18]. The main difference Discriminant analysis has been used as major tool for between these two techniques is that regression analysis predicting final results of students/disciplines based on deals with a continuous dependent variable, while various classifications in many researches [11-13]. discriminant analysis must have a discrete dependent A successful discrimination was made between two variable. groups of study by Ogum [14] who applied multivariate The mathematics of discriminant analysis is related analysis on scores of applicants admitted in university of very closely to the one-way MANOVA. In fact, the roles Nigeria medical school in the 1975/1976 academic of the variables are simply reversed. The classification session.Similar work is done by Okoli [15], who (factor) variable in the MANOVA becomes the dependent discriminated two groups based on academic scores and variable in discriminant analysis. The dependent variables found misclassifications of student scores using in the MANOVA become the independent variables in the classification rule. discriminant analysis.

This study is carried out to find some of the institutes Suppose you have data for K groups, with Nk misclassified as “having result below board average observations per group. Let N represent the total number result” may fall in “having result above board average of observations. Each observation consists of the result” group. Wrongly classified or misclassified measurements of p variables. The ith observation is institutes will be fish out with the help of discriminant represented by Xki . Let M represent the vector of means function and classification rule. of these variables across all groups and Mk the vector of means of observations in the kth group. MATERIALS AND METHODS Define three sums of squares and cross products

matrices, STW , S and S A as follows In this study, the data is obtained from managing body of Sargodha board which consists of Sargodha board 2nd year annual results 2014. The dependent variable is the overall college/higher secondary school (HSS) results (Y) and this result is divided into two categories: if the institute result is above board average result than group one and if the institute result is below board average result than group two. The overall SA = S- TW S

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Next, define two degrees of freedom values, df12 and df : RESULTS AND DISCUSSION df12 = K-1, df = N-K A discriminant function is a weighted average of the The purpose of the present study was to examine the values of the independent variables. The weights are relationship between institute annual academic selected so that the resulting weighted average separates performance under two categories (below/above board the observations into the groups. High values of the average result) and various institutes characteristics. Out average come from one group; low values of the average of 93 institutes included in our analysis we have 62 come from another group. The problem reduces to one of institutes showing result above board average and 31 finding the weights which, when applied to the data, best below board average. discriminate among groups according to some criterion. Mean scores on each variable is listed in group The solution reduces to finding the eigenvectors of means Table 1. Annual result of institutes with four −1 disciplines was high in group 2 on the average with mean SS. The canonical coefficients are the elements of WA values 82.1594, 80.1350, 71.8374 and 75.2887 for all these eigenvectors. disciplines respectively. However institute’s annual result when categorized as gender, districts and public or private A goodness-of-fit parameter, Wilks’ lambda, is defined as was almost equal in both groups on the average. follows: In order to access the importance of each predictor standardized and unstandardized coefficients are presented in Table 2. The constant term for S m 1 Λ=W =Π unstandardized model is -7.309 table 2 interpretation. S1j1= +λ Tj Univariate analysis is conducted to present the list of independent variables influencing the dependent variable. where j is the jth eigenvalue corresponding to the We can say six variables carry positive signs indicating eigenvector described above and m is the minimum of their significance contribution in discriminating the K- 1 and p. institutes with results above board average.On the other hand insignificant variable district carries a negative sign

The canonical correlation between the jth discriminant predicting the results below average result of function and the independent variables is related to institutes.Variables 2, 3, 4 and 5 are highly significant in λ j our analysis.The values used for calculating the cutting these eigenvalues as follows: rcj = 1 +λj scores for below average result and above average result The overall covariance matrix, T is given by: are -1.694 and 0.847 respectively. Table 3 provides the information about the overall significance of the model.Clustering of model under two The within group covariance matrix, W is given by: categories was significant. Unexplained error is 40% (Wilks' lambda:0.406). Out of total variation 59% of the The among group (or between group) covariance variability is explained by this model (canon matrix, A is given by: corr2 :0.59).Strong association is detected (canonical The linear discriminant functions are defined as: correlation coefficient: 0.77) between two groups namely set of all independent variables and group of board LDF= W−1 M kk average results scores of all institutes. The standardized canonical coefficients are given by: Table 4 shows that institutes individual vwij ij characteristics determine their annual results. This table represents two classification functions, one for each of where vij are the elements of V and wij are the elements of the two groups. Each function is represented vertically. W. Two equations are given below

The correlations between the independent variables Group 1: -25.492 + 0.160X12 + 0.136X + 0.088 X 3 + 0.050 X 4 and the canonical variates are given by: + 7.717 X5 + 2.575 X 67 + 4.779X (1)

p 1 Group 2: -42.290 + 0.184 X + 0.211 X + 0.127 X + 0.115 X Corrjk = ∑ vik w ji 1234 wij i1= + 9.796 X567 + 2.541 X + 5.817 X (2)

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Table 1: Group means Variables Group 1 Group 2 Overall

X1 69.8706 82.1594 78.0631

X2 50.9277 80.1350 70.3992

X3 50.5468 71.8374 64.7405

X4 46.9590 75.2887 65.8455

X5 1.2903 1.7742 1.6129

X6 3.1935 3.1290 3.1505

X7 1.1935 1.5000 1.3978 Count 31 62 93

Table 2: Summary of interpretive measures for discriminant analysis

Variables Unstandardized Standardized Wilks Lambda Discriminant Loading (Rank) df12 df Univariate F Ratio

X1 0.009 0.199 0.930 0.226 (6) 1 91 06.838

X2 0.029 0.567 0.657 0.597 (2) 1 91 47.537

X3 0.015 0.292 0.777 0.442 (3) 1 91 26.108

X4 0.025 0.415 0.597 0.678 (1) 1 91 61.381

X5 0.818 0.356 0.781 0.438 (4) 1 91 25.562

X6 -0.014 -0.015 0.999 -0.023 (7) 1 91 0.068*

X7 0.408 0.193 0.913 0.255 (5) 1 91 08.684 Group centroid below average result -1.694 Group centroid above average result 0.847 *insignificance

Table 3: Eigenvalues and multivariate test Function Eigenvalue % of Variance Cumulative % Canonical Correlation (Canonical Correlation)2 1 1.466a 100 100 0.771 0.59 Wilks Lambda Test Test of Function(s) Wilks Lambda Chi-square df Sig. 1 0.406 78.964 7 0.000 a. First 1 canonical discriminant functions were used in the analysis.

Table 4: Fisher’s linear discriminant functions classified correctly and three (4.8%) were incorrectly Variables Group 1 Group 2 classified as result below average. Hence, out of 93 cases, Constant -25.492 -42.290 85 were classified correctly, which means the accuracy of X 0.160 0.184 1 the application of the discriminant analysis is 91.40%. X2 0.136 0.211 Table 5 also helps in increasing the accuracy of X3 0.088 0.127

X4 0.050 0.115 assigning clusters. Assignment of row 9 to institute

X5 7.717 9.796 having result below average was actually misclassified. X6 2.575 2.541 However according to discriminant analysis it would X7 4.779 5.817 have been a better fit if this row was assigned to group of institute having result above average. Similarly Table 5: Classification count table for grouping misclassification of cluster is detected in row 18, 20, 22, 34, Predicted Group Membership Total 43, 51 and 90. (See appendix for misclassification rows) Actual Group 1 2 1 26(83.9) 05(16.1) 31(100) 2 03(4.8) 59(95.2) 62(100) CONCLUSION Total 29 64 93 The purpose of this study was to demonstrate that In Table 5 the accuracy of discriminant analysis is how discriminant analysis predict institute annual result presented. Out of ninety three institutes, thirty one above or below board average result on the basis of institutes with result below average, twenty six (83.9%) of institute’s demographical and structural characteristics. them classified correctly and five (16.1%) incorrectly Predictive equation is found for classifying new classified as result above average. Sixty two institutes individuals or interpreting the predictive equation to with result above average, fifty nine (95.2%) of them better understand the relationships that may exist among

216 World Appl. Sci. J., 33 (2): 213-219, 2015 the variables. Better accuracy is achieved by 9. Sohail, M.S. and S. Daud, 2009. Knowledge sharing reclassification of variables that were misclassified [19]. in higher education institutions: Perspectives from Successful discrimination is made between institutes with Malaysia. VINE: Journal Inf. Knowl. Management results below or above average. Clustering annual results System, 39(2): 125-142. of institutes under two categories is statistically 10. Ramayah, T., N.H. Ahmad, H.A. Halim, S.R.M. Zainal significant on the basis of discriminant analysis. and M.C. Lo, 2010. Discriminant Analysis: An Analyzing set of seven variables shows five of them Illustrated Example. African Journal of Business significantly help in discriminating between institutes with Management, 4(9): 1654-1667. result below or above board average. Therefore it is 11. Thomas, E.W., M.J. Marr, A. Thomas, R.M. Hume suggested to reclassified institutes who were and N. Walker, 1996. Using discriminant analysis to misclassified under results below board average result. identify students at risk. Frontiers in Education, IEEE publication 96CH35946, pp: 185-188. ACKNOWLEDGEMENT 12. Kasih, J. and S. Susanto, 2012. Predicting Students Final Results Through Discriminant Analysis. World The authors expresses their heartily gratitude to Dr. Transactions on Engineering and Technology Fatch Muhammad Malik current member of managing Education, 10(2): 144-147. body of Sargodha board for providing data from Sargodha 13. Divjak, B. and D. Oreski, 2009. Prediction of board. Academic Performance using Discriminant Analysis. Proceedings of the ITI 2009 31st International REFERENCES Conference on Information Technology Interfaces, June 22-25, 2009, Cavtat, Croatia, pp: 225-230. 1. Selingo and Brainard, 2001. Predicting Student 14. Ogum, G.E.O., 2002. An application of discriminant Outcomes Using Discriminant Function Analysis, RP analysis in university Admission (A case of the Group Proceedings, 2001: 163-173. university of medical school, 1975/76), Introduction 2. Akomolafe, M.J., 2013. Personality Characteristics as to methods of multivariate Analysis, pp :119-134. Predictors of Academic Performance of Secondary 15. Okoli, C.N., 2013. An application of Discriminant School Students. Mediterranean Journal of Social Analysis on University Matriculation Examination Sciences, 4(2): 657-664. Scores for Candidatues Admitted into Anamabra 3. www.bisesargodha.edu.pk State University. Journal of Natural Sciences 4. Sharma, S., 1992. Applied Multivariate Techniques. Research, 3(5): 182-191. Toronto: John Wiley and Sons, Inc. 16. Fisher, R.A., 1936. The use of Multiple 5. Betz, E.N., 1987. Use of Discriminant Analysis in Measurements in Taxonomic Problems. Annals of Counseling Psychology Research. Journal of Eugenies pp: 179-188. Counseling Phycology, 34(4): 393-403. 17. Johnson, R.A. and D.W. Wichern, 1992. Applied 6. Tuten, T.L. and D.J. Urban, 1999. Specific Responses Multivariate Statistical Analysis. Englewood Cliffs to Unmet Expectations: The Value of Linking New Jersey. Fishbein’s Theory of Reasoned Action and 18. Hedges, L.V., 1988. The meta-analysis of test validity Rusbult’s Investment Model, International Journal studies: Some new approaches. In H. Wainer & H. I. Management, 16(4): 484-489. Braun (Eds.). Test Validity, Erlbaum, pp: 191-212. 7. Bang, H., A.E. Ellinger, J. Hadimarcou and P.A. 19. Ramayah, T., M. Jantan and K. Chandramohan, 2004. Traichal, 2000. Consumer Concern, Knowledge, Belief Retrenchment Strategy in Human Resource and Attitude toward Renewable Energy:An Management: The Case of Voluntary Separation Application of the Reasoned Action Theory, Scheme (VSS). Asian Academy Management Journal, Psychol. Market, 17(6): 449-468. 9(2): 35-62. 8. Erimafa, J.T., A. Iduseri and L.W. Edokpal, 2009. Application of Discriminant Analysis to Predict the Class of Degree for Graduating Students in a University System. International Journal of Physical Sciences, 4(1): 16-21.

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Appendix: List of Institutes with Group Actual Predicted Sr. No. Institutes Name With Code Group Group 1 100466-GOVT. GIRLS H/S/S VIJH (SARGODHA) 1 1 2 100823-ALLAMA IQBAL PUBLIC HIGHER SECONDARY SCHOOL NAUSHERA (KHUSHAB) (Male) 2 2 3 101049-GOVT. H/S/S DHANDLA (BHAKKAR) (Male) 2 2 4 101095-AL-HUDA GIRLS H/S/S PIPLAN (MIANWALI) (Female) 2 2 5 200001-GOVT. COLLEGE BHAKKAR. (Male) 1 1 6 200002-GOVT. COLLEGE FOR WOMEN BHAKKAR. (Female) 2 2 7 200004-GOVT. GIRLS DEGREE COLLEGE DULLEWALA (BHAKKAR). (Female) 2 2 8 200010-GOVT. COLLEGE JAUHARABAD,(KHUSHAB). (Male) 1 1 9 200011-GOVT. JAUHAR COLLEGE FOR WOMEN JAUHARABAD,(KHUSHAB). (Female) 1 2 10 200022-GOVT. DEGREE COLLEGE, ISA KHEL (MIANWALI). (Male) 1 1 11 200023-GOVT. DEGREE COLLEGE (W) ISA KHEL (MIANWALI). (Female) 2 2 12 200027-GOVT. DEGREE COLLEGE LIAQUATABAD (MIANWALI). (Male) 1 1 13 200028-GOVT. COLLEGE FOR WOMEN LIAQUATABAD (MIANWALI). (Female) 2 2 14 200029-GOVT. COLLEGE MIANWALI. (Male) 1 1 15 200030-GOVT. COLLEGE FOR WOMEN MIANWALI. (Female) 2 2 16 200034-GOVT. COLLEGE ,(SARGODHA). (Male) 1 1 17 200035-GOVT. COLLEGE FOR WOMEN BHALWAL,(SARGODHA). (Female) 2 2 18 200036-GOVT. DEGREE COLLEGE ,(SARGODHA). (Male) 1 2 19 200039-GOVT. DEGREE COLLEGE DULLEWALA (BHAKKAR). (Male) 1 1 20 200042-GOVT. COLLEGE FOR WOMEN,CHAK NO 36/SB(SARGODHA) (Female) 2 1 21 200052-GOVT. DEGREE COLLEGE CHAK NO.90 SB (SARGODHA). (Male) 2 2 22 200061-GOVT. COLLEGE FOR WOMEN, FAROOKA.(SARGODHA) (Female) 1 2 23 200062-GOVT. COLLEGE FAROOKA.(SARGODHA). (Male) 1 1 24 200071-GOVT. COLLEGE FOR WOMEN (SARGODHA) (Female) 2 2 25 200074-GOVT. POST GRADUATE COLLEGE FOR WOMEN SARGODHA. (Female) 2 2 26 200075-GOVT. COLLEGE FOR WOMEN FAROOQ COLONY SARGODHA. (Female) 2 2 27 200076-GOVT. AMBALA MUSLIM COLLEGE SARGODHA. (Male) 1 1 28 200079-GOVT. COLLEGE FOR WOMEN,SAHIWAL(SARGODHA). (Female) 2 2 29 200082-GOVT. COLLEGE SHAHPUR SADDAR,(SARGODHA). (Male) 1 1 30 200083-ALFAUZ INTERNATIONAL COLLEGE, JAUHARABAD (KHUSHAB). (Female) 2 2 31 200084-GOVT. DEGREE COLLEGE (SARGODHA) (Male) 1 1 32 200089-PUNJAB COLLEGE OF INFORMATION TECH SARGODHA. (Male) 2 2 33 200090-GOVT. DEGREE COLLEGE FOR WOMEN BLOCK NO.23-A SARGODHA. (Female) 1 1 34 200095-ITM COLLEGE 8 UNIVERSITY ROAD SARGODHA. (Male) 2 1 35 200097-PUNJAB COLLEGE FOR WOMEN SARGODHA. (Female) 2 2 36 200106-GOVT. GIRLS H/S/S P A F COLONY MIANWALI. (Female) 2 2 37 200117-DAR-E-ARQAM MODEL GIRLS COLLEGE BHALWAL SARGODHA (Female) 2 2 38 200136-DAR-E-ARQAM MODEL COLLEGE (BOYS) SARGODHA. (Male) 2 2 39 200142-GOVT. DEGREE COLLEGE BHAGTANWALA (SARGODHA) (Male) 1 1 40 200143-IQRA GIRLS COLLEGE SARGODHA. (Female) 2 2 41 200146-AL SUFFAH GIRLS COLLEGE SARGODHA. (Female) 2 2 42 200155-GOVT. DEGREE COLLEGE DARYA KHAN (BHAKKAR) (Male) 2 2 43 200156-GOVT. GIRLS DEGREE COLLEGE KALLURKOT (BHAKKAR) (Female) 1 2 44 200158-DAR-E-ARQAM MODEL COLLEGE (GIRLS) SARGODHA CANTT. (Female) 2 2 45 200163-GOVT. DEGREE COLLEGE FOR (W) BHAGTANWALA (SARGODHA). (Female) 2 2 46 200165-GOVT. COLLEGE FOR WOMEN SHAHPUR SADAR (SARGODHA) (Female) 2 2 47 200166-GOVT. COLLEGE FOR WOMEN DARYA KHAN (BHAKKAR) (Female) 2 2 48 200170-GOVT. DEGREE COLLEGE (KHUSHAB) (Male) 1 1 49 200177-GOVT. COLLEGE FOR WOMEN KHUSHAB (Female) 2 2 50 200187-ILM COLLEGE OF COMMERCE (FOR WOMEN) SARGODHA. (Female) 2 2 51 200188-ILM COLLEGE FOR BOYS SARGODHA. (Male) 2 1 52 200190-THE SUPERIOR COLLEGE FOR WOMEN, SARGODHA. (Female) 2 2 53 200191-THE SUPERIOR COLLEGE OF COMMERCE (BOYS) SARGODHA. (Male) 2 2 54 200192-HI-AIMS GIRLS COLLEGE JAUHARABAD (KHUSHAB) (Female) 2 2 55 200193-ITM COLLEGE OF COMMERCE FOR WOMEN 4 UNIVERSITY RAOD SARGODHA (Female) 2 2 56 200196-GOVT. COLLEGE FOR WOMEN KAMAR MASHANI (MIANWALI) (Female) 2 2 57 200197-GOVT. COLLEGE FOR WOMEN NOSHERA (KHUSHAB) (Female) 2 2 58 200198-GOVT. BOYS COLLEGE BIN HAFIZ JI (MIANWALI) (Male) 1 1 59 200201-COMPREHENSIVE COLLEGE OF COMMERCE & MANAGEMENT GIRLS (SARGODHA) (Female) 2 2 60 200202-COMPREHENSIVE COLLEGE OF COMMERCE & MANAGEMENT BOYS (SARGODHA) (Male) 2 2 61 200203-SCHOLERS COLLEGE FOR WOMEN BHALWAL (SARGODHA) (Female) 2 2 62 200204-SCHOLERS COLLEGE BHALWAL (SARGODHA) (Male) 1 1 63 200206-PUNJAB COLLGE OF SCIENCE JAUHARABAD (KHUSHAB) (Male) 2 2 64 200207-PUNJAB COLLGE FOR WOMEN JAUHARABAD (KHUSHAB) (Female) 2 2

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Appendix: List of Institutes with Group Actual Predicted Sr. No. Institutes Name With Code Group Group 65 202002-GOVT. COLLEGE FOR WOMEN KOTMOMIN SARGODHA (Female) 2 2 66 202003-GOVT. COLLEGE KOTMOMIN SARGODHA (Male) 1 1 67 202006-NEW SUPERIOR SCIENCE COLLEGE,SILLANWALI (SARGODHA) (Male) 1 1 68 202015-NATIONAL COLLEGE OF COMPUTER SCIENCE GIRLS (SARGODHA) (Female) 1 1 69 202016-GOVT. MIAN MUHAMMAD NAWAZ SHARIF DEGREE COLLEGE FOR BOYS SARGODHA. (Male) 1 1 70 202019-GOVT. DEGREE COLLEGE FOR WOMEN BHERA. (Female) 2 2 71 202020-GOVT.DEGREE COLLEGE FOR WOMEN, DAUD KHEL, MIANWALI. (Female) 1 1 72 202021-GOVT.DEGREE COLLEGE FOR WOMEN, WAN BHACHRAN, MIANWALI. (Female) 2 2 73 202022-GOVT.DEGREE COLLEGE FOR WOMEN, MUSA KHEL, MIANWALI. (Female) 2 2 74 202024-PIONEER SCIENCE COLLEGE FOR GIRLS BHALWAL, SARGODHA. (Female) 2 2 75 202025-PIONEER SCIENCE COLLEGE FOR BOYS BHALWAL, SARGODHA. (Male) 1 1 76 202026-PUNJAB COLLEGE OF SCIENCE NEAR RAILWAY PHATAK BHALWAL, (SARGODHA) (Male) 2 2 77 202028-NISA GIRLS COLLEGE 91-C SATELLITE TOWN SARGODHA (Female) 2 2 78 202029-SUPERIOR COLLEGE DARYA KHAN ROAD BHAKKAR (Male) 2 2 79 202030-SUPERIOR COLLEGE FOR WOMEN DARYA KHAN ROAD BHAKKAR (Female) 2 2 80 202034-PUNJAB COLLEGE FOR WOMEN, BHAKKAR (Female) 2 2 81 300123-GOVT. HIGHER SECONDARY SCHOOL ASHRAF WALA(BHAKKAR) (Male) 2 2 82 300185-KCP MODEL H/S/S GIRLS KCP COLONY CHOWK JAUHARABAD (KHUSHAB) (Female) 2 2 83 300212-COL. MUHAMMAD SHER TAMIR-E-MILAT (GIRLS) H/S/S MITHA TIWANA (KHUSHAB) (Female) 2 2 84 300433-GOVT. GIRLS HIGHER SECONDARY SCHOOL, NEHANG (SARGODHA) (Female) 2 2 85 300434-GOVT. GIRLS HIGHER SECONDARY SCHOOL, MIDH RANJHA SARGODHA (Female) 2 2 86 300435-GOVT. GIRLS HIGHER SECONDARY SCHOOL, 46/SB (SARGODHA). (Female) 2 2 87 300478-GOVT. GIRLS HIGHER SECONDARY SCHOOL HAIDERABAD TOWN (SARGODHA) (Female) 2 2 88 300562-GOVT. HIGHER SECONDARY SCHOOL NEHANG (SARGODHA). (Male) 1 1 89 300567-GOVT. HIGHER SECONDARY SCHOOL CHAK NO.88 SB (SARGODHA). (Male) 1 1 90 300713-COMMUNITY GIRLS H/S/S KHABAKI (KHUSHAB). (Female) 1 2 91 300896-JINNAH ENGLISH PUBLIC GIRLS H/S/S JAHAN KHAN (BHAKKAR} (Female) 1 1 92 300905-GOVT. NATIONAL MODEL GIRLS HIGHER SECONDARY SCHOOL PAF, SARGODHA (Female) 2 2 93 300909-WAPDA GIRLS H/S/S CHASHMA MIANWALI (Female) 2 2

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