You are now a sqlite data analyst, and you are given a database schema as follows:

    【Schema】
    【DB_ID】 college_completion
【Schema】
# Table: institution_details
[
(unitid:INTEGER, Primary Key, Examples: [100654, 100663, 100690]),
(chronname:TEXT, Examples: [Alabama A&M University]),
(city:TEXT, Examples: [Normal, Birmingham, Montgomery]),
(state:TEXT, Examples: [Alabama, Alaska, Arizona]),
(level:TEXT, Examples: [4-year, 2-year]),
(control:TEXT, Examples: [Public]),
(basic:TEXT, Examples: [Masters Colleges and Universities--larger programs]),
(hbcu:TEXT, Examples: [X, NULL]),
(flagship:TEXT, Examples: [NULL, X]),
(long_x:REAL, Examples: [-86.568502, -86.80917, -86.17401]),
(lat_y:REAL, Examples: [34.783368, 33.50223, 32.362609]),
(site:TEXT, Examples: [www.aamu.edu/]),
(student_count:INTEGER, Examples: [4051, 11502, 322]),
(awards_per_value:REAL, Examples: [14.2, 20.9, 29.9]),
(awards_per_state_value:REAL, Examples: [18.8, 17.8, 15.9]),
(awards_per_natl_value:REAL, Examples: [21.5, 22.5, 16.5]),
(exp_award_value:INTEGER, Examples: [105331, 136546, 58414]),
(exp_award_state_value:INTEGER, Examples: [75743, 92268, 42194]),
(exp_award_natl_value:INTEGER, Examples: [66436, 101725, 37780]),
(exp_award_percentile:INTEGER, Examples: [90, 97, 30]),
(ft_pct:REAL, Examples: [93.8, 72.7, 62.7]),
(fte_value:INTEGER, Examples: [3906, 10032, 294]),
(fte_percentile:INTEGER, Examples: [33, 67, 12]),
(med_sat_value:TEXT, Examples: [823, 1146, NULL]),
(med_sat_percentile:TEXT, Examples: [0, 84, NULL]),
(aid_value:INTEGER, Examples: [7142, 6088, 2540]),
(aid_percentile:INTEGER, Examples: [72, 50, 1]),
(endow_value:TEXT, Examples: [NULL, 24136, 302]),
(endow_percentile:TEXT, Examples: [NULL, 93, 1]),
(grad_100_value:REAL, Examples: [10.0, 29.4, 0.0]),
(grad_100_percentile:INTEGER, Examples: [15, 67, 0]),
(grad_150_value:REAL, Examples: [29.1, 53.5, 66.7]),
(grad_150_percentile:INTEGER, Examples: [14, 66, 72]),
(pell_value:REAL, Examples: [71.2, 35.1, 68.4]),
(pell_percentile:INTEGER, Examples: [98, 39, 91]),
(retain_value:REAL, Examples: [63.1, 80.2, 37.5]),
(retain_percentile:INTEGER, Examples: [17, 70, 2]),
(ft_fac_value:REAL, Examples: [82.8, 92.4, 67.2]),
(ft_fac_percentile:INTEGER, Examples: [89, 98, 71]),
(vsa_year:TEXT, Examples: [2010, 2011, NULL]),
(vsa_grad_after4_first:TEXT, Examples: [14.7, 22.3, NULL]),
(vsa_grad_elsewhere_after4_first:TEXT, Examples: [2, 2.9, NULL]),
(vsa_enroll_after4_first:TEXT, Examples: [36.5, 34.2, NULL]),
(vsa_enroll_elsewhere_after4_first:TEXT, Examples: [16.1, 19.2, NULL]),
(vsa_grad_after6_first:TEXT, Examples: [33, 42.6, NULL]),
(vsa_grad_elsewhere_after6_first:TEXT, Examples: [5.3, 10.5, NULL]),
(vsa_enroll_after6_first:TEXT, Examples: [12.5, 7.9, NULL]),
(vsa_enroll_elsewhere_after6_first:TEXT, Examples: [14.6, 13.1, NULL]),
(vsa_grad_after4_transfer:TEXT, Examples: [15.7, NULL, 0]),
(vsa_grad_elsewhere_after4_transfer:TEXT, Examples: [1.5, NULL, 0]),
(vsa_enroll_after4_transfer:TEXT, Examples: [40.9, NULL, 0]),
(vsa_enroll_elsewhere_after4_transfer:TEXT, Examples: [17.2, NULL, 0]),
(vsa_grad_after6_transfer:TEXT, Examples: [36.4, NULL, 0]),
(vsa_grad_elsewhere_after6_transfer:TEXT, Examples: [5.6, NULL, 0]),
(vsa_enroll_after6_transfer:TEXT, Examples: [17.2, NULL, 0]),
(vsa_enroll_elsewhere_after6_transfer:TEXT, Examples: [11.1, NULL, 0]),
(similar:TEXT),
(state_sector_ct:INTEGER, Examples: [13, 16, 25]),
(carnegie_ct:INTEGER, Examples: [386, 106, 252]),
(counted_pct:TEXT, Examples: [99.7|07, 56.0|07, 100.0|07]),
(nicknames:TEXT, Examples: [NULL, UAB, UAH]),
(cohort_size:INTEGER, Examples: [882, 1376, 3])
]
# Table: state_sector_grads
[
(stateid:INTEGER, Examples: [1, 2, 4]),
(state:TEXT, Examples: [Alabama, Alaska, Arizona]),
(state_abbr:TEXT, Examples: [AL, AK, AZ]),
(control:TEXT, Examples: [Private for-profit]),
(level:TEXT, Examples: [4-year, 2-year]),
(year:INTEGER, Examples: [2011, 2012, 2013]),
(gender:TEXT, Examples: [B, F, M]),
(race:TEXT, Examples: [A, Ai, B]),
(cohort:TEXT, Examples: [4y bach, 4y other, 2y all]),
(grad_cohort:TEXT, Examples: [0, 1, 51]),
(grad_100:TEXT, Examples: [0, 2, 15]),
(grad_150:TEXT, Examples: [0, 3, 18]),
(grad_100_rate:TEXT, Examples: [NULL, 0, 3.9]),
(grad_150_rate:TEXT, Examples: [NULL, 0, 5.9]),
(grad_cohort_ct:INTEGER, Examples: [9, 16, 13])
]
# Table: institution_grads
[
(unitid:INTEGER, Examples: [100760, 101028, 101143]),
(year:INTEGER, Examples: [2011, 2012, 2013]),
(gender:TEXT, Examples: [B, M, F]),
(race:TEXT, Examples: [X, W, B]),
(cohort:TEXT, Examples: [2y all, 4y other, 4y bach]),
(grad_cohort:TEXT, Examples: [446, 185, 261]),
(grad_100:TEXT, Examples: [73, NULL, 40]),
(grad_150:TEXT, Examples: [105, 40, 65]),
(grad_100_rate:TEXT, Examples: [16.4, NULL, 6.7]),
(grad_150_rate:TEXT, Examples: [23.5, 21.6, 24.9])
]
# Table: state_sector_details
[
(stateid:INTEGER, Primary Key, Examples: [0, 1, 2]),
(state:TEXT, Examples: [United States, Alabama, Alaska]),
(state_post:TEXT, Examples: [U.S., Ala., Alaska]),
(level:TEXT, Primary Key, Examples: [2-year, 4-year]),
(control:TEXT, Primary Key, Examples: [Private for-profit]),
(schools_count:INTEGER, Examples: [632, 1180, 527]),
(counted_pct:TEXT, Examples: [NULL, 61, 62]),
(awards_per_state_value:TEXT, Examples: [NULL, 18.8, 17.8]),
(awards_per_natl_value:REAL, Examples: [21.5, 22.5, 24.6]),
(exp_award_state_value:TEXT, Examples: [NULL, 75743, 92268]),
(exp_award_natl_value:INTEGER, Examples: [66436, 101725, 38763]),
(state_appr_value:TEXT, Examples: [NULL, 290.68, 496.78]),
(state_appr_rank:TEXT, Examples: [NULL, 11, 2]),
(grad_rate_rank:TEXT, Examples: [23, 18, 8]),
(awards_per_rank:TEXT, Examples: [NULL, 42, 49])
]
【Foreign keys】
state_sector_grads.state=institution_details.state
state_sector_grads.stateid=state_sector_details.stateid
institution_grads.unitid=institution_details.unitid
state_sector_details.state=institution_details.state

    【Question】
    What is the average SAT value for incoming students in all of the schools located in the state with the lowest state appropriations to higher education in fiscal year 2011 per resident? average = DIVIDE(SUM(med_sat_value), SUM(chronname)); SAT value for incoming students refers to med_sat_value; lowest state appropriations to higher education in fiscal year 2011 per resident refers to MIN(state_appr_value);

    【Evidence】
    average = DIVIDE(SUM(med_sat_value), SUM(chronname)); SAT value for incoming students refers to med_sat_value; lowest state appropriations to higher education in fiscal year 2011 per resident refers to MIN(state_appr_value);

    Please read and understand the database schema carefully, and generate an executable SQL based on the user's question and evidence. 

SQL: SELECT AVG(t1.med_sat_value) FROM institution_details AS T1 INNER JOIN state_sector_details AS T2 ON t1.state = t2.state ORDER BY t2.state_appr_value LIMIT 1