{
  "title": "Median (Statistics) - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "The median divides the data into:", "options": {"A": "Two equal parts", "B": "Four equal parts", "C": "Ten equal parts", "D": "Three equal parts"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "For ungrouped data, median is the:", "options": {"A": "Middle value when arranged", "B": "Average of all values", "C": "Most frequent value", "D": "First value"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "For odd number of observations n, median position =", "options": {"A": "(n+1)/2", "B": "n/2", "C": "(n-1)/2", "D": "n/2 + 1"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "For even number of observations, median is:", "options": {"A": "Average of two middle values", "B": "First middle value", "C": "Second middle value", "D": "Sum of two middle values"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "For grouped data, median class is where cumulative frequency reaches:", "options": {"A": "N/2", "B": "N", "C": "N/4", "D": "3N/4"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "In median formula, 'l' represents:", "options": {"A": "Lower limit of median class", "B": "Upper limit of median class", "C": "Length of class", "D": "Lower limit of first class"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "In median formula, 'cf' represents:", "options": {"A": "Cumulative frequency before median class", "B": "Frequency of median class", "C": "Total frequency", "D": "Cumulative frequency after median class"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "In median formula, 'f' represents:", "options": {"A": "Frequency of median class", "B": "Total frequency", "C": "Cumulative frequency", "D": "Class frequency"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "In median formula, 'h' represents:", "options": {"A": "Class width of median class", "B": "Height", "C": "Hypotenuse", "D": "Highest value"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "For data: 2,4,6,8,10, median is:", "options": {"A": "6", "B": "5", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "For data: 3,1,7,5,9, after arranging, median is:", "options": {"A": "5", "B": "3", "C": "7", "D": "6"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "For data: 10,20,30,40, median is:", "options": {"A": "25", "B": "20", "C": "30", "D": "35"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "If n=7, median position is:", "options": {"A": "4th", "B": "3.5th", "C": "3rd", "D": "5th"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "If n=10, median is average of:", "options": {"A": "5th and 6th values", "B": "4th and 5th values", "C": "6th and 7th values", "D": "3rd and 4th values"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Median is a measure of:", "options": {"A": "Central tendency", "B": "Dispersion", "C": "Correlation", "D": "Regression"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Median is not affected by:", "options": {"A": "Extreme values", "B": "Middle values", "C": "Frequency", "D": "Class width"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "For frequency distribution, N =", "options": {"A": "∑f", "B": "∑fx", "C": "∑f²", "D": "∑x"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "To find median graphically, we use:", "options": {"A": "Ogive", "B": "Histogram", "C": "Frequency polygon", "D": "Bar graph"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "If all observations are equal, median equals:", "options": {"A": "That value", "B": "Zero", "C": "Mean", "D": "Mode"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "For data: 5,5,5,5,5, median is:", "options": {"A": "5", "B": "10", "C": "25", "D": "0"}, "correct_answer": "A"},
    
    {"id": 21, "difficulty": "medium", "question": "For data: 12,15,18,20,22,25,28, median is:", "options": {"A": "20", "B": "18", "C": "22", "D": "19"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Classes: 0-10:5, 10-20:8, 20-30:12. Find median class.", "options": {"A": "20-30", "B": "10-20", "C": "0-10", "D": "None"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Given: Class 0-10:4, 10-20:6, 20-30:10, 30-40:5. N/2 =", "options": {"A": "12.5", "B": "12", "C": "13", "D": "25"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "For classes: 0-10:3, 10-20:7, 20-30:10, median =", "options": {"A": "22", "B": "20", "C": "18", "D": "24"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Classes: 10-20:5, 20-30:8, 30-40:7. If l=20, cf=5, f=8, h=10, median =", "options": {"A": "26.25", "B": "25", "C": "27.5", "D": "28.75"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Data: 5,8,12,15,18,21,24. Median is:", "options": {"A": "15", "B": "12", "C": "18", "D": "16.5"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "For N=25, median class is where cumulative frequency ≥", "options": {"A": "12.5", "B": "13", "C": "12", "D": "25"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Classes: 0-20:10, 20-40:15, 40-60:25. cf before median class =", "options": {"A": "10", "B": "25", "C": "15", "D": "35"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Given: Class 0-10:2, 10-20:5, 20-30:8, 30-40:5. Median =", "options": {"A": "23.75", "B": "22.5", "C": "25", "D": "21.25"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "For data: 3,7,2,9,5,8,4, after arranging:", "options": {"A": "5", "B": "4", "C": "6", "D": "7"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Classes: 100-200:5, 200-300:10, 300-400:15. N/2 =", "options": {"A": "15", "B": "30", "C": "25", "D": "20"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "If l=30, cf=20, f=15, h=10, N=50, median =", "options": {"A": "33.33", "B": "30", "C": "35", "D": "32.5"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Classes: 0-5:4, 5-10:6, 10-15:10, 15-20:5. Median class:", "options": {"A": "10-15", "B": "5-10", "C": "15-20", "D": "0-5"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Data: 12,15,11,18,14,16,13,17. Median:", "options": {"A": "14.5", "B": "14", "C": "15", "D": "13.5"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "For N=40, cf before median class=18, f=12, l=25, h=5, median =", "options": {"A": "25.83", "B": "26.67", "C": "27.5", "D": "24.17"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Classes: 20-30:3, 30-40:7, 40-50:10, 50-60:5. cf for class 40-50 =", "options": {"A": "10", "B": "13", "C": "20", "D": "25"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "If median=35, l=30, cf=25, f=20, h=10, find N.", "options": {"A": "100", "B": "80", "C": "90", "D": "110"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Classes: 0-10:8, 10-20:12, 20-30:15. Median =", "options": {"A": "21.33", "B": "20.5", "C": "22.67", "D": "19.8"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Data: 25,30,22,28,35,26,32. Median:", "options": {"A": "28", "B": "27", "C": "29", "D": "26"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "For class 40-50 as median class, l=40, cf=30, f=25, h=10, N=100, median =", "options": {"A": "44", "B": "42", "C": "46", "D": "48"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Classes: 0-100:2, 100-200:5, 200-300:8, 300-400:5. Median class:", "options": {"A": "200-300", "B": "100-200", "C": "300-400", "D": "0-100"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "If N=60, median class has cf ≥", "options": {"A": "30", "B": "31", "C": "29", "D": "60"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Classes: 10-15:4, 15-20:6, 20-25:8, 25-30:2. l for median class =", "options": {"A": "20", "B": "15", "C": "25", "D": "10"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Data: 42,38,45,40,43,39,44,41. Median:", "options": {"A": "41.5", "B": "41", "C": "42", "D": "40.5"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Classes: 0-20:10, 20-40:15, 40-60:20, 60-80:5. N/2 =", "options": {"A": "25", "B": "50", "C": "30", "D": "20"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "If l=50, cf=40, f=30, h=20, median=55, find N.", "options": {"A": "140", "B": "120", "C": "160", "D": "180"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Classes: 0-10:5, 10-20:10, 20-30:15, 30-40:10. cf before median class =", "options": {"A": "15", "B": "25", "C": "30", "D": "10"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Data: 55,60,52,58,63,57,59,61. Median:", "options": {"A": "58.5", "B": "58", "C": "59", "D": "57.5"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Classes: 100-150:3, 150-200:7, 200-250:10, 250-300:5. h for median class =", "options": {"A": "50", "B": "100", "C": "150", "D": "200"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "If median=28, l=20, cf=15, f=12, h=10, find N.", "options": {"A": "50", "B": "60", "C": "40", "D": "70"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Classes: 0-5:2, 5-10:4, 10-15:6, 15-20:3. Median =", "options": {"A": "11.25", "B": "10.83", "C": "12.5", "D": "9.67"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Data: 18,22,15,25,20,23,17,19,24. Median:", "options": {"A": "20", "B": "19.5", "C": "21", "D": "20.5"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "Classes: 30-40:4, 40-50:8, 50-60:12, 60-70:6. Median class:", "options": {"A": "50-60", "B": "40-50", "C": "60-70", "D": "30-40"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "If N=80, cf before median class=35, f=20, l=45, h=15, median =", "options": {"A": "48.75", "B": "47.5", "C": "50.25", "D": "46.2"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "Classes: 0-50:5, 50-100:10, 100-150:15, 150-200:10. cf for class 100-150 =", "options": {"A": "15", "B": "25", "C": "30", "D": "40"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Data: 7,3,9,5,11,6,8,4,10. After arranging, median:", "options": {"A": "7", "B": "6", "C": "8", "D": "6.5"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Classes: 20-25:3, 25-30:5, 30-35:7, 35-40:5. l for median class =", "options": {"A": "30", "B": "25", "C": "35", "D": "20"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "If median=42.5, l=40, cf=30, f=25, h=10, find N.", "options": {"A": "100", "B": "90", "C": "110", "D": "120"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Classes: 0-10:8, 10-20:12, 20-30:15, 30-40:5. N =", "options": {"A": "40", "B": "50", "C": "45", "D": "35"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "Data: 33,37,31,35,39,34,36,38,32. Median:", "options": {"A": "35", "B": "34.5", "C": "36", "D": "35.5"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "Classes: 0-20:6, 20-40:9, 40-60:12, 60-80:3. Median class:", "options": {"A": "40-60", "B": "20-40", "C": "60-80", "D": "0-20"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "If l=100, cf=80, f=40, h=50, N=200, median =", "options": {"A": "112.5", "B": "110", "C": "115", "D": "107.5"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Classes: 5-15:4, 15-25:6, 25-35:8, 35-45:2. cf before median class =", "options": {"A": "10", "B": "4", "C": "14", "D": "18"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "Data: 45,50,42,48,53,47,49,51,44. Median:", "options": {"A": "48", "B": "47.5", "C": "49", "D": "48.5"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Classes: 0-25:5, 25-50:10, 50-75:15, 75-100:10. h for median class =", "options": {"A": "25", "B": "50", "C": "75", "D": "100"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "If median=65, l=60, cf=55, f=20, h=10, find N.", "options": {"A": "150", "B": "140", "C": "160", "D": "170"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "Classes: 0-100:2, 100-200:8, 200-300:12, 300-400:8. Median =", "options": {"A": "250", "B": "240", "C": "260", "D": "230"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "Data: 12,8,15,10,18,13,16,11,14,9. Median:", "options": {"A": "12.5", "B": "12", "C": "13", "D": "11.5"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Classes: 10-20:3, 20-30:7, 30-40:10, 40-50:5. cf for class 30-40 =", "options": {"A": "10", "B": "13", "C": "20", "D": "25"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "If N=120, cf before median class=50, f=30, l=35, h=5, median =", "options": {"A": "38.33", "B": "37.5", "C": "39.17", "D": "36.8"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "Classes: 0-5:4, 5-10:8, 10-15:12, 15-20:6. Median class:", "options": {"A": "10-15", "B": "5-10", "C": "15-20", "D": "0-5"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Data: 22,25,19,28,23,26,20,24,27,21. After arranging, median:", "options": {"A": "23.5", "B": "23", "C": "24", "D": "22.5"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "Classes: 20-30:5, 30-40:8, 40-50:12, 50-60:5. l for median class =", "options": {"A": "40", "B": "30", "C": "50", "D": "20"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "If median=75.5, l=70, cf=60, f=25, h=10, find N.", "options": {"A": "130", "B": "120", "C": "140", "D": "150"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Classes: 0-10:10, 10-20:15, 20-30:20, 30-40:15. N/2 =", "options": {"A": "30", "B": "60", "C": "25", "D": "35"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Data: 35,40,32,38,43,37,39,41,34,36. Median:", "options": {"A": "37.5", "B": "37", "C": "38", "D": "36.5"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "Classes: 0-50:4, 50-100:10, 100-150:16, 150-200:10. cf before median class =", "options": {"A": "14", "B": "4", "C": "20", "D": "30"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "If l=45, cf=30, f=20, h=15, median=48, find N.", "options": {"A": "100", "B": "90", "C": "110", "D": "120"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "Classes: 5-10:3, 10-15:5, 15-20:7, 20-25:5. Median =", "options": {"A": "16.79", "B": "15.83", "C": "17.14", "D": "16.25"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "Data: 28,32,25,30,35,27,33,29,31,26. Median:", "options": {"A": "29.5", "B": "29", "C": "30", "D": "28.5"}, "correct_answer": "A"},
    
    {"id": 81, "difficulty": "hard", "question": "Classes: 0-10:5, 10-20:8, 20-30:12, 30-40:x, 40-50:5. If median=28 and N=50, find x.", "options": {"A": "20", "B": "15", "C": "18", "D": "22"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "For data with median=42.5, if all values increased by 10, new median:", "options": {"A": "52.5", "B": "42.5", "C": "32.5", "D": "47.5"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "Classes: 0-20:10, 20-40:15, 40-60:f, 60-80:10. If median=45 and N=70, find f.", "options": {"A": "35", "B": "30", "C": "25", "D": "40"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "If median of 15 numbers is 25 and each number multiplied by 2, new median:", "options": {"A": "50", "B": "25", "C": "12.5", "D": "75"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "Classes: 10-20:4, 20-30:6, 30-40:10, 40-50:8. If frequencies in first two classes doubled, new median (original median=35):", "options": {"A": "33.75", "B": "35", "C": "36.25", "D": "32.5"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "For grouped data, if class intervals changed from 0-10,10-20 to 0-5,5-10,10-15,15-20 with same total frequency, median:", "options": {"A": "Remains same", "B": "Doubles", "C": "Halves", "D": "Changes slightly"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Classes: 0-100:2, 100-200:5, 200-300:8, 300-400:5. If upper limit of each class increased by 50, new median (original median=250):", "options": {"A": "275", "B": "250", "C": "225", "D": "300"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "If median=35 and Q1=25, Q3=45, what percent of data lies between 25 and 45?", "options": {"A": "50%", "B": "25%", "C": "75%", "D": "100%"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "Classes: 0-10:a, 10-20:10, 20-30:15, 30-40:10. If median=24 and N=50, find a.", "options": {"A": "15", "B": "12", "C": "18", "D": "20"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "For ungrouped data: x, 2x, 3x, 4x, 5x. Median:", "options": {"A": "3x", "B": "2x", "C": "4x", "D": "x"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Classes: 20-30:5, 30-40:8, 40-50:12, 50-60:5. If each frequency increased by 2, new median (original median=43.33):", "options": {"A": "43.33", "B": "44.17", "C": "42.5", "D": "43.75"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "If median position for n observations is 12.5th, then n =", "options": {"A": "24", "B": "25", "C": "23", "D": "26"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Classes: 0-20:10, 20-40:15, 40-60:25, 60-80:10. If class intervals changed to 0-10,10-20,...,70-80 with frequencies distributed proportionally, new median:", "options": {"A": "Approximately same", "B": "Doubles", "C": "Halves", "D": "Increases by 10"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "For data with median 50, if each value decreased by 20%, new median:", "options": {"A": "40", "B": "50", "C": "30", "D": "60"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Classes: 0-10:4, 10-20:6, 20-30:10, 30-40:x. If median=27.5 and N=35, find x.", "options": {"A": "15", "B": "12", "C": "10", "D": "8"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "If median of first n natural numbers is 12.5, then n =", "options": {"A": "24", "B": "25", "C": "23", "D": "26"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "Classes: 100-120:5, 120-140:8, 140-160:12, 160-180:5. If all class marks increased by 10, new median:", "options": {"A": "Increases by 10", "B": "Remains same", "C": "Decreases by 10", "D": "Doubles"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "For symmetric distribution, median equals:", "options": {"A": "Mean", "B": "Mode", "C": "Both A and B", "D": "Neither"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "Classes: 0-5:2, 5-10:4, 10-15:6, 15-20:3. If frequencies in first and last classes swapped, new median:", "options": {"A": "11.67", "B": "11.25", "C": "12.5", "D": "10.83"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "If median of a, b, c is 15 and a<b<c, and a=10, c=20, then b =", "options": {"A": "15", "B": "10", "C": "20", "D": "25"}, "correct_answer": "A"}
  ]
}