{
  "title": "Cumulative Frequency - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Cumulative frequency is always? ➕", "options": {"A": "Decreasing", "B": "Non-decreasing", "C": "Constant", "D": "Random"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "To find median from cumulative frequency curve, we use ___ percentile. 📈", "options": {"A": "25th", "B": "50th", "C": "75th", "D": "100th"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "The last value in 'less than' cumulative frequency table is equal to? 📊", "options": {"A": "Highest frequency", "B": "Total frequency", "C": "Lowest frequency", "D": "Mean frequency"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "Cumulative frequency is calculated by? 🧮", "options": {"A": "Adding frequencies", "B": "Subtracting frequencies", "C": "Multiplying frequencies", "D": "Dividing frequencies"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "For 'more than' cumulative frequency, we start from? ⬇️", "options": {"A": "Lowest class", "B": "Highest class", "C": "Middle class", "D": "Any class"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "The cumulative frequency curve is also called? 📉", "options": {"A": "Histogram", "B": "Ogive", "C": "Pie chart", "D": "Bar graph"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "If frequency of class 0-10 is 5 and 10-20 is 7, cumulative frequency for 'less than 20' is? 🔢", "options": {"A": "5", "B": "7", "C": "12", "D": "2"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "Cumulative frequency distribution shows? 👀", "options": {"A": "Frequency of each class", "B": "Running total of frequencies", "C": "Relative frequency", "D": "Class boundaries"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "To draw 'less than' ogive, we plot points with coordinates? 📍", "options": {"A": "(upper limit, cumulative freq)", "B": "(lower limit, cumulative freq)", "C": "(midpoint, cumulative freq)", "D": "(class width, cumulative freq)"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "The median from ogive is found at cumulative frequency = N/2, where N is? Σ", "options": {"A": "Number of classes", "B": "Total frequency", "C": "Highest frequency", "D": "Class width"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "If total frequency is 50, median corresponds to cumulative frequency? 🤔", "options": {"A": "25", "B": "50", "C": "12.5", "D": "100"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "First quartile Q1 corresponds to cumulative frequency? 📊", "options": {"A": "N/4", "B": "N/2", "C": "3N/4", "D": "N"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "A cumulative frequency table can help find? 🎯", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "All of these"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "If cumulative frequency for class 'less than 30' is 40 and for 'less than 40' is 65, frequency of class 30-40 is? 🔄", "options": {"A": "25", "B": "40", "C": "65", "D": "105"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "In 'more than' ogive, the curve is? 📈", "options": {"A": "Increasing", "B": "Decreasing", "C": "Constant", "D": "U-shaped"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "For grouped data, cumulative frequency is calculated for? 📦", "options": {"A": "Each observation", "B": "Class intervals", "C": "Midpoints", "D": "Frequencies only"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "The point where both ogives intersect gives? ✖️", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "Range"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "If N=100, third quartile Q3 is at cumulative frequency? 3️⃣", "options": {"A": "25", "B": "50", "C": "75", "D": "100"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "Cumulative frequency curve is always? 📉", "options": {"A": "Smooth", "B": "Step-like", "C": "Straight line", "D": "Curved upward"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "To find number of students scoring less than 50 marks, we use? 📝", "options": {"A": "Frequency table", "B": "Cumulative frequency", "C": "Pictograph", "D": "Bar graph"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "Given: Class 0-10: f=5, 10-20: f=12, 20-30: f=20, 30-40: f=8. Cumulative frequency for 'less than 30' is? 🧮", "options": {"A": "20", "B": "32", "C": "37", "D": "45"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "For data with total frequency 80, median class is where cumulative frequency first exceeds? 🔍", "options": {"A": "20", "B": "40", "C": "60", "D": "80"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "If 'less than' cumulative frequencies are 10, 25, 45, 60, 70, total frequency N is? Σ", "options": {"A": "70", "B": "60", "C": "45", "D": "10"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "From ogive, median is found by drawing horizontal at ___ to meet curve, then vertical to x-axis. ↔️", "options": {"A": "N/2", "B": "N/4", "C": "3N/4", "D": "N"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Classes: 0-5,5-10,10-15. 'More than' cumulative frequency for 5 is? ⬆️", "options": {"A": "f(0-5)+f(5-10)+f(10-15)", "B": "f(5-10)+f(10-15)", "C": "f(10-15)", "D": "Total frequency"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "For quartile deviation, we need Q1 & Q3 from cumulative frequency at? 📏", "options": {"A": "N/4 & 3N/4", "B": "N/2 & N", "C": "N/3 & 2N/3", "D": "N/5 & 4N/5"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "If cumulative frequency just greater than 32.5 is 45, median lies in class with cumulative frequency? 🎯", "options": {"A": "32.5", "B": "45", "C": "Class before 45", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "To find number of students scoring between 40-60 marks, we subtract cumulative frequencies of? ➖", "options": {"A": "60 & 40", "B": "60 & 30", "C": "70 & 40", "D": "80 & 40"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Given less than cf: (10,5), (20,12), (30,25), (40,30). Frequency of class 20-30 is? 🔢", "options": {"A": "7", "B": "12", "C": "13", "D": "5"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "For drawing ogive, we need? ✏️", "options": {"A": "Class boundaries & cf", "B": "Midpoints & f", "C": "Class limits & f", "D": "Class size & f"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "If N=60, lower quartile is value corresponding to cumulative frequency? 🔽", "options": {"A": "15", "B": "30", "C": "45", "D": "60"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "The median from ogive is more accurate than from formula for? ✅", "options": {"A": "Ungrouped data", "B": "Grouped data", "C": "Both", "D": "Neither"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "If 'more than' cf for 20 is 65 and for 30 is 45, frequency of class 20-30? 📊", "options": {"A": "20", "B": "25", "C": "45", "D": "65"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "For percentile P_k, we find cumulative frequency first exceeding? 🎯", "options": {"A": "kN/100", "B": "k/N", "C": "N/k", "D": "100k/N"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "The intersection point of 'less than' and 'more than' ogives has y-coordinate? 📍", "options": {"A": "N/2", "B": "N", "C": "0", "D": "N/4"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Given: Class 10-20: f=8, cf=8; 20-30: f=12, cf=20; 30-40: f=10, cf=30. Median class? 🎯", "options": {"A": "10-20", "B": "20-30", "C": "30-40", "D": "40-50"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "To find mode from cumulative frequency curve, we use? 🔍", "options": {"A": "Cannot find directly", "B": "N/2 point", "C": "Intersection of ogives", "D": "Highest frequency point"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "If cumulative frequency polygon is drawn, points are joined by? 📈", "options": {"A": "Straight lines", "B": "Curves", "C": "Dots", "D": "Bars"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "For symmetrical distribution, median from ogive lies at? ⚖️", "options": {"A": "Left end", "B": "Center", "C": "Right end", "D": "Anywhere"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "Given total frequency 50, if Q1=22.5 and Q3=47.5, interquartile range? 📐", "options": {"A": "25", "B": "22.5", "C": "47.5", "D": "70"}, "correct_answer": "A"},

    {"id": 41, "difficulty": "hard", "question": "For data with classes 0-10,10-20,... and frequencies 5,15,25,30,20,5. 'Less than' cf for 40? 📊", "options": {"A": "95", "B": "100", "C": "75", "D": "80"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "If 'less than' ogive and 'more than' ogive intersect at (42.5, 50), median is? ❌", "options": {"A": "42.5", "B": "50", "C": "92.5", "D": "7.5"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "Given cumulative frequency distribution: x<10:4, x<20:9, x<30:15, x<40:20. Frequency of class 20-30? 🔢", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "hard", "question": "To find median graphically, we draw horizontal at y=N/2 to meet ogive, then vertical to x-axis. This gives? 📏", "options": {"A": "Exact median", "B": "Approximate median", "C": "Modal class", "D": "Mean"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "hard", "question": "For a distribution, median=32, mean=30. Ogive will be skewed? 📊", "options": {"A": "Positively", "B": "Negatively", "C": "Symmetrical", "D": "Cannot say"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "If cumulative frequency curve is steep, it indicates? 📈", "options": {"A": "Low frequency", "B": "High frequency", "C": "No frequency", "D": "Constant frequency"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "hard", "question": "Given: Classes 0-5,5-10,10-15 with 'more than' cf: 50,40,25,5. Frequency of 10-15? 🔄", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "hard", "question": "For percentile calculation from ogive, horizontal line is drawn at y=? 📐", "options": {"A": "kN/100", "B": "k", "C": "N/k", "D": "100/k"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "If 'less than' cf for 30 is 28 and for 40 is 45, and N=60, median class? 🎯", "options": {"A": "20-30", "B": "30-40", "C": "40-50", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "hard", "question": "The difference between 'less than' and 'more than' ogives at any x is? ➖", "options": {"A": "Frequency of that class", "B": "Total frequency", "C": "N/2", "D": "Constant"}, "correct_answer": "D"},
    {"id": 51, "difficulty": "hard", "question": "To find number of observations between a and b using ogive, we find? 🔍", "options": {"A": "cf(b)-cf(a)", "B": "cf(a)-cf(b)", "C": "cf(a)+cf(b)", "D": "cf(a)×cf(b)"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "For continuous data, ogive is drawn by plotting ___ against cumulative frequency. 📍", "options": {"A": "Upper limits", "B": "Lower limits", "C": "Class marks", "D": "Class boundaries"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "hard", "question": "If ogive is S-shaped, distribution is? 📊", "options": {"A": "Normal", "B": "Skewed", "C": "Uniform", "D": "Random"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "Given N=100, Q1=22, Q3=68. Quartile coefficient of dispersion? 📐", "options": {"A": "0.46", "B": "0.51", "C": "0.34", "D": "0.23"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "hard", "question": "For exponential distribution, ogive shape is? 📈", "options": {"A": "Straight line", "B": "Rapidly increasing", "C": "S-shaped", "D": "U-shaped"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "hard", "question": "To estimate median from ogive, accuracy depends on? 🎯", "options": {"A": "Scale of graph", "B": "Smoothness of curve", "C": "Class width", "D": "All of these"}, "correct_answer": "D"},
    {"id": 57, "difficulty": "hard", "question": "If cumulative frequency curve has plateau, it indicates? ⏸️", "options": {"A": "Zero frequency class", "B": "High frequency class", "C": "Missing data", "D": "Error"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "For open-ended classes, ogive can still be drawn if we assume? 🤔", "options": {"A": "Class boundaries", "B": "Class marks", "C": "Class widths", "D": "Frequencies"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "The median from 'less than' ogive and 'more than' ogive should? ✅", "options": {"A": "Be equal", "B": "Differ", "C": "Be reciprocal", "D": "Be unrelated"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "Given: Class 0-10: f=5, cf=5; 10-20: f=?, cf=15; 20-30: f=10, cf=25. Missing frequency? ❓", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "B"}
  ]
}