{
  "title": "Graphical Representation Ogive (Statistics) - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "An ogive is a graph that represents:", "options": {"A": "Cumulative frequencies", "B": "Individual frequencies", "C": "Class marks", "D": "Class intervals"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "For drawing a less than ogive, we plot:", "options": {"A": "Upper limits on x-axis", "B": "Lower limits on x-axis", "C": "Class marks on x-axis", "D": "Frequencies on x-axis"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "The point where both ogives intersect gives:", "options": {"A": "Mean", "B": "Mode", "C": "Median", "D": "Range"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "In a more than ogive, cumulative frequencies are:", "options": {"A": "Increasing", "B": "Decreasing", "C": "Constant", "D": "Zero"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "The x-coordinate of the intersection point of less than and more than ogives represents:", "options": {"A": "Median class", "B": "Median value", "C": "Modal class", "D": "Mean value"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Which cumulative frequency curve is always decreasing?", "options": {"A": "Less than ogive", "B": "More than ogive", "C": "Both are decreasing", "D": "Neither is decreasing"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "To draw an ogive, we need:", "options": {"A": "Only frequencies", "B": "Cumulative frequencies", "C": "Class marks only", "D": "Class intervals only"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "The shape of an ogive is typically:", "options": {"A": "Bell-shaped", "B": "U-shaped", "C": "S-shaped", "D": "Straight line"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "In a less than ogive, the curve is:", "options": {"A": "Always increasing", "B": "Always decreasing", "C": "First increasing then decreasing", "D": "First decreasing then increasing"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "The total frequency is represented on ogive at:", "options": {"A": "Starting point of x-axis", "B": "End point of y-axis", "C": "Starting point of y-axis", "D": "Intersection point"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "For class 0-10 with frequency 5, the less than cumulative frequency for upper limit 10 is:", "options": {"A": "0", "B": "5", "C": "10", "D": "15"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "The y-axis in an ogive represents:", "options": {"A": "Class intervals", "B": "Cumulative frequencies", "C": "Frequencies", "D": "Class marks"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "To find median graphically, we draw:", "options": {"A": "Only less than ogive", "B": "Only more than ogive", "C": "Both ogives", "D": "Frequency polygon"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "An ogive is also called:", "options": {"A": "Frequency polygon", "B": "Histogram", "C": "Cumulative frequency curve", "D": "Bar graph"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "For class interval 20-30, in less than ogive we plot point at x =:", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "In more than ogive, we plot points corresponding to:", "options": {"A": "Upper limits", "B": "Lower limits", "C": "Class marks", "D": "Midpoints"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "The cumulative frequency for the last class in less than ogive equals:", "options": {"A": "Zero", "B": "Total frequency", "C": "First frequency", "D": "Last frequency"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "Which graphical method helps find median?", "options": {"A": "Histogram", "B": "Frequency polygon", "C": "Ogive", "D": "Bar graph"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "For a more than ogive, the first point plotted has coordinates:", "options": {"A": "(0, total frequency)", "B": "(lower limit of first class, total frequency)", "C": "(upper limit of first class, 0)", "D": "(midpoint, frequency)"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "The less than ogive curve always starts from:", "options": {"A": "(0,0)", "B": "(first upper limit, 0)", "C": "(first lower limit, total frequency)", "D": "(0, total frequency)"}, "correct_answer": "A"},
    
    {"id": 21, "difficulty": "medium", "question": "Given: Class 0-10: freq 5, 10-20: freq 7, 20-30: freq 8. What is the less than cumulative frequency for class 20-30?", "options": {"A": "8", "B": "12", "C": "15", "D": "20"}, "correct_answer": "D"},
    {"id": 22, "difficulty": "medium", "question": "For the data: Class 0-5:4, 5-10:6, 10-15:10, 15-20:8, what is the more than cumulative frequency for class 5-10?", "options": {"A": "24", "B": "18", "C": "28", "D": "22"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "The less than cumulative frequency table for classes 0-10, 10-20, 20-30 has values 8, 15, 25. What is the frequency of class 10-20?", "options": {"A": "7", "B": "8", "C": "15", "D": "10"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "From an ogive, the median is found to be 25.5. What does this mean?", "options": {"A": "50% of data is below 25.5", "B": "25.5% of data is below 50", "C": "75% of data is below 25.5", "D": "25.5 is the mean"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Given cumulative frequencies: Less than 10:5, Less than 20:12, Less than 30:20. What is the frequency of class 20-30?", "options": {"A": "5", "B": "7", "C": "8", "D": "12"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "If total frequency is 50 and median from ogive is 28, how many observations are less than 28?", "options": {"A": "25", "B": "28", "C": "50", "D": "22"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "For data: Class 0-20:10, 20-40:15, 40-60:25. What is the more than cumulative frequency for class 20-40?", "options": {"A": "40", "B": "25", "C": "50", "D": "15"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "The intersection point of ogives has coordinates (25, 30). If total frequency is 60, what is the median?", "options": {"A": "25", "B": "30", "C": "60", "D": "15"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "In a less than ogive, points are (10,5), (20,12), (30,20). What is the frequency of class 10-20?", "options": {"A": "5", "B": "7", "C": "12", "D": "8"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "For a more than ogive, points are (0,50), (10,45), (20,30). What is the frequency of class 0-10?", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Given: Class 0-5:3, 5-10:7, 10-15:10, 15-20:6. What is the less than cumulative frequency for upper limit 15?", "options": {"A": "10", "B": "13", "C": "20", "D": "16"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "If median from ogive is 42.5 and total frequency is 80, how many observations are above 42.5?", "options": {"A": "40", "B": "42.5", "C": "80", "D": "37.5"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "The less than cumulative frequency for class 30-40 is 45 and for 40-50 is 60. What is the frequency of class 40-50?", "options": {"A": "15", "B": "45", "C": "60", "D": "105"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "For more than ogive, points are (20,40), (30,25), (40,10). What is the total frequency?", "options": {"A": "40", "B": "25", "C": "10", "D": "65"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "In a less than ogive, if point (25, 35) means:", "options": {"A": "35 observations are less than 25", "B": "25 observations are less than 35", "C": "25% observations are less than 35", "D": "35% observations are less than 25"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Given frequency distribution: 0-10:5, 10-20:8, 20-30:12, 30-40:5. What is the less than cumulative frequency for 30?", "options": {"A": "25", "B": "30", "C": "35", "D": "40"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "For a more than ogive starting at (0, N), the last point will be:", "options": {"A": "(last upper limit, 0)", "B": "(last lower limit, 0)", "C": "(last upper limit, N)", "D": "(0, 0)"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "If less than cumulative frequencies are 10, 25, 45, 60, the frequencies are:", "options": {"A": "10,15,20,15", "B": "10,25,45,60", "C": "10,35,80,140", "D": "10,15,25,30"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "From ogive, quartile Q1 is found as 18. This means:", "options": {"A": "25% data below 18", "B": "50% data below 18", "C": "75% data below 18", "D": "18% data below 25"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "The less than ogive and more than ogive always intersect at y-coordinate equal to:", "options": {"A": "Total frequency/2", "B": "Total frequency", "C": "0", "D": "Median class frequency"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Given: Class 0-100: 5, 100-200: 12, 200-300: 8. What is more than cumulative frequency for class 100-200?", "options": {"A": "20", "B": "25", "C": "13", "D": "8"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "If total frequency is 40, from ogive Q3 = 48. How many observations are between median and Q3?", "options": {"A": "10", "B": "20", "C": "30", "D": "40"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "For classes with unequal widths, ogive can be drawn:", "options": {"A": "Only with equal class intervals", "B": "Only with adjusted frequencies", "C": "Directly without any change", "D": "Cannot be drawn"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "medium", "question": "The less than cumulative frequency for class 50-60 is 75 and for 60-70 is 90. Frequency of 60-70 is:", "options": {"A": "15", "B": "75", "C": "90", "D": "165"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "From more than ogive: (10,50), (20,35), (30,15). Frequency of 20-30 is:", "options": {"A": "15", "B": "20", "C": "35", "D": "50"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "medium", "question": "If N=50 and median=28 from ogive, then from less than ogive at x=28, y≈:", "options": {"A": "25", "B": "28", "C": "50", "D": "22"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Given less than cf: 10, 22, 40, 55, 60. Total frequency is:", "options": {"A": "60", "B": "55", "C": "40", "D": "10"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "For finding median graphically, we draw horizontal line from y=N/2 to intersect ogive, then drop perpendicular to x-axis. This gives:", "options": {"A": "Median", "B": "Mode", "C": "Mean", "D": "Q1"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "In a more than ogive, if point (15, 40) exists, it means:", "options": {"A": "40 observations ≥15", "B": "15 observations ≥40", "C": "40% observations ≥15", "D": "15% observations ≥40"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "The difference between two consecutive less than cumulative frequencies gives:", "options": {"A": "Class frequency", "B": "More than cf", "C": "Relative frequency", "D": "Cumulative frequency"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "For data: 0-10:5, 10-20:8, 20-30:12, 30-40:7, 40-50:3. What is less than cf for 40?", "options": {"A": "30", "B": "35", "C": "38", "D": "40"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "If from ogive, 75th percentile = 54, then:", "options": {"A": "75% data ≤54", "B": "54% data ≤75", "C": "25% data ≤54", "D": "54 observations ≤75"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "Given more than cf: (0,80), (10,65), (20,40), (30,15). Frequency of 10-20 is:", "options": {"A": "15", "B": "25", "C": "40", "D": "65"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "For less than ogive, points plotted are:", "options": {"A": "(upper limits, less than cf)", "B": "(lower limits, less than cf)", "C": "(midpoints, frequencies)", "D": "(upper limits, frequencies)"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "If less than cf for 20 is 18 and for 30 is 32, frequency of 20-30 is:", "options": {"A": "14", "B": "18", "C": "32", "D": "50"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "From a less than ogive, to find number of observations below 25, we:", "options": {"A": "Find x where y=25", "B": "Find y where x=25", "C": "Find intersection at x=25", "D": "Draw vertical at x=25"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "medium", "question": "Given: Class 0-5:2, 5-10:5, 10-15:8, 15-20:5. More than cf for 10 is:", "options": {"A": "15", "B": "13", "C": "18", "D": "20"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "medium", "question": "The ogive curve is always:", "options": {"A": "Smooth", "B": "Broken line", "C": "Straight line", "D": "Can be any shape"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "If N=60, from less than ogive at x=35, y=42. Percentage of observations below 35 is:", "options": {"A": "70%", "B": "42%", "C": "60%", "D": "35%"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "For more than ogive, if point (25, 30) and next (35, 15), frequency of 25-35 is:", "options": {"A": "15", "B": "25", "C": "30", "D": "45"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "Given less than cf: 5, 14, 26, 35, 40. Frequency of third class is:", "options": {"A": "9", "B": "12", "C": "26", "D": "35"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "To find median from only less than ogive, we locate y=N/2, then find corresponding x. This x is:", "options": {"A": "Median", "B": "Approximate median", "C": "Exact median", "D": "Modal value"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "If more than cf for 40 is 28 and for 50 is 15, frequency of 40-50 is:", "options": {"A": "13", "B": "28", "C": "15", "D": "43"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "For class intervals 0-10, 10-20, 20-30, the x-coordinates for less than ogive are:", "options": {"A": "10,20,30", "B": "5,15,25", "C": "0,10,20", "D": "10,15,20"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Given: N=50, from ogive Q1=22. Number of observations below 22 is approximately:", "options": {"A": "12.5", "B": "22", "C": "25", "D": "50"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "In a more than ogive, curve is drawn by joining points:", "options": {"A": "Smoothly by freehand", "B": "With straight lines", "C": "With dotted lines", "D": "With histogram bars"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "If less than cf for 15 is 24 and for 25 is 42, frequency of 15-25 is:", "options": {"A": "18", "B": "24", "C": "42", "D": "66"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "From both ogives, if intersection point is (m, N/2), then m is:", "options": {"A": "Median", "B": "Mean", "C": "Mode", "D": "Midrange"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Given more than cf table: ≥0:45, ≥10:38, ≥20:25, ≥30:10. Frequency of 20-30 is:", "options": {"A": "15", "B": "25", "C": "10", "D": "35"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "For less than ogive, we start plotting from point:", "options": {"A": "(0,0)", "B": "(first upper limit, 0)", "C": "(0, first frequency)", "D": "(first lower limit, 0)"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "If from ogive, 80% of observations are below 56, then 56 is:", "options": {"A": "80th percentile", "B": "20th percentile", "C": "Median", "D": "Q3"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Given less than cf: 4, 10, 18, 25, 30. More than cf for lower limit of third class is:", "options": {"A": "20", "B": "18", "C": "12", "D": "22"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "The ogive helps find median without using formula when:", "options": {"A": "Data is grouped", "B": "Data is ungrouped", "C": "Class intervals are equal", "D": "Frequencies are small"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "If N=40 and from less than ogive at x=28, y=26, then percentage above 28 is:", "options": {"A": "35%", "B": "65%", "C": "26%", "D": "28%"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "For more than ogive, first point has coordinates:", "options": {"A": "(lower limit of first class, N)", "B": "(0, N)", "C": "(upper limit of first class, N)", "D": "(0,0)"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Given: Class 0-100:10, 100-200:15, 200-300:12, 300-400:8. Less than cf for 300 is:", "options": {"A": "37", "B": "45", "C": "30", "D": "25"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "If Q1=18 from ogive and N=48, number of observations between Q1 and median is:", "options": {"A": "12", "B": "18", "C": "24", "D": "30"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "The less than ogive is always:", "options": {"A": "Non-decreasing", "B": "Non-increasing", "C": "Constant", "D": "Decreasing then increasing"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "From more than ogive: (10,50), (20,35), (30,20), (40,5). Total frequency is:", "options": {"A": "50", "B": "35", "C": "20", "D": "5"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "If median from ogive is 32.5 and total observations=60, then observations ≤32.5 is:", "options": {"A": "30", "B": "32.5", "C": "60", "D": "27.5"}, "correct_answer": "A"},
    
    {"id": 81, "difficulty": "hard", "question": "For data with classes 0-10, 10-20, 20-30, 30-40 with frequencies 5, 12, 18, 5 respectively. If median from ogive is 22.5, what is the less than cumulative frequency at x=20?", "options": {"A": "17", "B": "22", "C": "25", "D": "30"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "Given: More than ogive points: (0,100), (10,85), (20,60), (30,30), (40,10). What is the median?", "options": {"A": "25", "B": "30", "C": "27.5", "D": "32.5"}, "correct_answer": "C"},
    {"id": 83, "difficulty": "hard", "question": "For a distribution, less than ogive gives points: (10,8), (20,22), (30,40), (40,52), (50,60). What is the frequency of modal class if mode=25?", "options": {"A": "14", "B": "18", "C": "22", "D": "12"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "From both ogives, intersection point is (27.5, 45). If total frequency is 90, what is the exact median?", "options": {"A": "27.5", "B": "45", "C": "22.5", "D": "50"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "Given: Class 0-20:10, 20-40:f, 40-60:25, 60-80:15. If median from ogive is 45, find f. (N=70)", "options": {"A": "20", "B": "15", "C": "25", "D": "30"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "For a less than ogive, points are: (100,15), (200,40), (300,65), (400,80), (500,90). What is Q1?", "options": {"A": "166.67", "B": "150", "C": "180", "D": "200"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "If from ogive, 30th percentile=18 and 70th percentile=34, what is the interpercentile range?", "options": {"A": "16", "B": "52", "C": "26", "D": "34"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "Given more than cf: (10,120), (20,105), (30,80), (40,50), (50,20). If Q3=42.5, what is the total frequency?", "options": {"A": "120", "B": "105", "C": "80", "D": "50"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "For data with classes 0-5,5-10,10-15,15-20 with frequencies a,b,c,d. If less than cf at 10 is 25 and at 15 is 45, and median=12.5, find c. (N=60)", "options": {"A": "20", "B": "25", "C": "15", "D": "30"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "From a less than ogive, at x=25, y=30 and at x=35, y=55. If N=100, what is the frequency of class 25-35?", "options": {"A": "25", "B": "30", "C": "55", "D": "85"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Given: More than ogive points: (0,80), (20,65), (40,40), (60,20), (80,5). Find D7 (70th percentile).", "options": {"A": "56", "B": "60", "C": "52", "D": "48"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "For a distribution, less than ogive gives: (10,12), (20,28), (30,52), (40,68), (50,80). If mode lies in class 20-30, what is the lower limit of modal class?", "options": {"A": "20", "B": "30", "C": "25", "D": "28"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "From both ogives intersection at (32.5, 37.5). If total frequency=75, what percent of observations lie between 25 and 32.5?", "options": {"A": "25%", "B": "50%", "C": "37.5%", "D": "32.5%"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "Given: Class 0-10:5, 10-20:8, 20-30:12, 30-40:x, 40-50:7. If median from ogive=28, find x. (N=50)", "options": {"A": "18", "B": "15", "C": "12", "D": "10"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "For less than ogive: (100,20), (200,45), (300,70), (400,85), (500,100). Find P90.", "options": {"A": "460", "B": "440", "C": "420", "D": "480"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "If from ogive, Q1=15, Q3=35, and median=25, what is the quartile deviation?", "options": {"A": "10", "B": "20", "C": "25", "D": "15"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "Given more than cf: (0,200), (50,180), (100,140), (150,80), (200,30). Find median class.", "options": {"A": "100-150", "B": "150-200", "C": "50-100", "D": "0-50"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "For data: 0-20:10, 20-40:15, 40-60:25, 60-80:20, 80-100:10. From ogive, find number of observations between 30 and 70.", "options": {"A": "48", "B": "52", "C": "60", "D": "45"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "If from less than ogive, at x=22.5, y=30 and N=80, what percentile is 22.5?", "options": {"A": "37.5th", "B": "30th", "C": "22.5th", "D": "27.5th"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "Given: Less than ogive points: (10,8), (20,24), (30,48), (40,66), (50,80). If mode=28, find frequency of modal class.", "options": {"A": "24", "B": "18", "C": "30", "D": "22"}, "correct_answer": "A"}
  ]
}