{
  "title": "Histograms and Frequency Polygons - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "📊 What type of data is a histogram used for? ", "options": {"A": "Qualitative data", "B": "Ungrouped discrete data", "C": "Continuous grouped data", "D": "Data over time"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "📈 In a histogram, the bars are drawn... ", "options": {"A": "with equal spaces between them", "B": "without any space between them", "C": "as separate circles", "D": "only on the y-axis"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "🔢 What is plotted on the x-axis of a histogram? ", "options": {"A": "Frequencies", "B": "Class intervals", "C": "Class marks", "D": "Cumulative frequency"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "📊 What is plotted on the y-axis of a histogram? ", "options": {"A": "Class intervals", "B": "Frequencies", "C": "Class marks", "D": "Percentages"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "📐 In a histogram, the area of each bar represents the... ", "options": {"A": "class mark", "B": "frequency of that class", "C": "upper limit", "D": "range"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "📈 A frequency polygon is created by joining the mid-points of the tops of bars of a... ", "options": {"A": "pie chart", "B": "bar graph", "C": "histogram", "D": "pictograph"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "🎯 The mid-point of a class interval is called the... ", "options": {"A": "class limit", "B": "class mark", "C": "class size", "D": "class frequency"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "📊 To draw a frequency polygon, we plot points with coordinates (class mark, ?). ", "options": {"A": "class size", "B": "frequency", "C": "upper limit", "D": "lower limit"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "📈 After plotting points for a frequency polygon, we join them with... ", "options": {"A": "curved lines", "B": "straight line segments", "C": "dotted lines", "D": "no lines"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "🔍 How is a frequency polygon made a closed figure? ", "options": {"A": "By joining the first and last point", "B": "By connecting to the x-axis at class marks before first and after last", "C": "By drawing a circle around it", "D": "It is never closed"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "✅ A histogram and frequency polygon can be drawn on the same graph. (True/False) ", "options": {"A": "True", "B": "False", "C": "Only for pie charts", "D": "Only for bar graphs"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "📊 For equal class intervals, in a histogram, the height of a bar is proportional to... ", "options": {"A": "class mark", "B": "frequency", "C": "class size", "D": "cumulative frequency"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "📐 If class intervals are 0-10, 10-20, 20-30, the class marks are... ", "options": {"A": "0, 10, 20", "B": "5, 15, 25", "C": "10, 20, 30", "D": "5, 10, 15"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "🎯 What is the class mark for the interval 15-25? ", "options": {"A": "15", "B": "20", "C": "25", "D": "40"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "📈 A frequency polygon looks like a... ", "options": {"A": "series of bars", "B": "many-sided figure", "C": "line graph", "D": "circle"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "📊 The frequency polygon is used to show the... ", "options": {"A": "shape of the distribution", "B": "exact class limits", "C": "total frequency", "D": "class size only"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "🔢 In a histogram, if a class has frequency 0, the bar... ", "options": {"A": "is very tall", "B": "has zero height", "C": "is not drawn", "D": "is drawn with spaces"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "📐 The class size for intervals 5-15, 15-25, 25-35 is... ", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "✅ A histogram can be drawn for discrete data if we convert it to continuous intervals. (True/False) ", "options": {"A": "True", "B": "False", "C": "Only for qualitative data", "D": "Never"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "🎯 The total area under a histogram represents the... ", "options": {"A": "total frequency", "B": "mean", "C": "range", "D": "class size"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "📊 For classes 10-20 (freq 8), 20-30 (freq 12), what is plotted for the first bar in a histogram? ", "options": {"A": "A bar from 10 to 20 of height 8", "B": "A bar from 10 to 30 of height 20", "C": "A point at (15, 8)", "D": "A bar from 0 to 10"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "📈 To draw a frequency polygon for the above data, the first point plotted is at... ", "options": {"A": "(10, 8)", "B": "(20, 12)", "C": "(15, 8)", "D": "(25, 12)"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "🔢 For a frequency polygon, we add an extra class before the first and after the last with frequency... ", "options": {"A": "equal to the first and last frequency", "B": "zero", "C": "equal to the mean", "D": "one"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "📊 If the class intervals are 0-5, 5-10, 10-15, and frequencies are 4, 6, 5, what is the total area of the histogram? (Class size=5) ", "options": {"A": "15", "B": "75", "C": "20", "D": "100"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "🎯 For unequal class intervals, we adjust the height of bars using... ", "options": {"A": "class mark", "B": "frequency density = freq/class width", "C": "cumulative frequency", "D": "percentage"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "📐 Classes: 0-10 (freq 5), 10-30 (freq 20). What is the frequency density for the second class? ", "options": {"A": "20", "B": "1", "C": "10", "D": "2"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "📈 A frequency polygon can be drawn directly from data without a histogram by plotting (class mark, frequency). (True/False) ", "options": {"A": "True", "B": "False, you always need the histogram first", "C": "False, you need a pie chart", "D": "False, you need raw data"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "🔍 If the class marks are 25, 35, 45 and frequencies are 10, 15, 12, what is the class size? ", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "📊 In a histogram, if class width is 5 and frequency is 15, the height of the bar is... ", "options": {"A": "3", "B": "15", "C": "75", "D": "depends on scale"}, "correct_answer": "D"},
    {"id": 30, "difficulty": "medium", "question": "🎯 Which is a characteristic of a frequency polygon? ", "options": {"A": "It is a curve", "B": "It is made of bars", "C": "It starts and ends on the x-axis", "D": "It represents percentages"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "📈 For data: Class marks: 22, 27, 32, 37; Freq: 6, 8, 10, 4. What is the first class interval if class size is 5? ", "options": {"A": "20-25", "B": "19.5-24.5", "C": "22-27", "D": "17-22"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "🔢 The frequency polygon is useful for comparing... ", "options": {"A": "two or more distributions", "B": "only one distribution", "C": "qualitative data", "D": "only large data sets"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "📊 If a histogram has a bar with very high frequency, the frequency polygon will... ", "options": {"A": "have a peak at that class mark", "B": "be flat", "C": "go downwards", "D": "become a circle"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "🎯 To find the mode from a histogram, we look for the bar with... ", "options": {"A": "the largest area", "B": "the greatest height", "C": "the smallest width", "D": "the darkest color"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "📐 For classes 30-40, 40-50, 50-60, the extra class added before for frequency polygon has class mark... ", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "📈 The sum of frequencies in a frequency polygon is equal to... ", "options": {"A": "area under the polygon", "B": "sum of heights of bars", "C": "total frequency", "D": "class size sum"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "🔍 If the total area of a histogram is 200 sq units and total frequency is 40, what is the scale? (Assume equal class width) ", "options": {"A": "1 unit area = 0.2 frequency", "B": "5 unit area = 1 frequency", "C": "Cannot determine", "D": "Area not related to frequency"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "✅ A histogram gives a better visual of frequency distribution than a frequency polygon. (True/False) ", "options": {"A": "True, as it shows area", "B": "False, both are good for different purposes", "C": "False, polygon is always better", "D": "True, only histogram is valid"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "📊 When class intervals are in integers like 1-10, 11-20, we treat them as... for histogram. ", "options": {"A": "0.5-10.5, 10.5-20.5", "B": "1-10, 11-20", "C": "1-10.5, 11-20.5", "D": "0-10, 10-20"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "🎯 In a frequency polygon, the mid-points of the tops of histogram bars are joined. What are these mid-points? ", "options": {"A": "Class limits", "B": "Class marks", "C": "Class frequencies", "D": "Class boundaries"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "hard", "question": "📊 Draw a histogram for: 0-10 (5), 10-20 (12), 20-30 (8), 30-40 (5). Total area? (Class size=10) ", "options": {"A": "30", "B": "300", "C": "100", "D": "50"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "📈 For the above data, what are the coordinates for the third point in the frequency polygon? ", "options": {"A": "(20, 12)", "B": "(25, 8)", "C": "(30, 8)", "D": "(15, 12)"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "hard", "question": "🔢 For unequal classes: 0-5 (freq 10), 5-15 (freq 30), 15-20 (freq 15). Adjusted height for second bar? ", "options": {"A": "30", "B": "3", "C": "15", "D": "1.5"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "hard", "question": "🎯 If a frequency polygon has points (5,2), (15,6), (25,10), (35,4), what is the total frequency? ", "options": {"A": "22", "B": "20", "C": "18", "D": "16"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "📐 For classes 10-19, 20-29, 30-39, what are the class boundaries? ", "options": {"A": "10-20, 20-30, 30-40", "B": "9.5-19.5, 19.5-29.5, 29.5-39.5", "C": "10-19, 20-29, 30-39", "D": "10.5-19.5, 20.5-29.5, 30.5-39.5"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "hard", "question": "📊 In a histogram, if the class 20-30 has frequency 18 and class width 10, what is its area? ", "options": {"A": "18", "B": "180", "C": "1.8", "D": "28"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "hard", "question": "🔍 For a frequency polygon, the extra class before the first has class mark = first class mark - class size. If first class mark is 25 and size 10, what is it? ", "options": {"A": "15", "B": "20", "C": "35", "D": "5"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "📈 Given class boundaries 0.5-10.5, 10.5-20.5 and frequencies 7, 13, what is the class mark of the second class? ", "options": {"A": "10.5", "B": "15.5", "C": "20.5", "D": "15"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "hard", "question": "🎯 To compare two frequency distributions, we can draw... ", "options": {"A": "two histograms on same graph", "B": "two frequency polygons on same graph", "C": "a pie chart for each", "D": "Both A and B"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "hard", "question": "📊 If a histogram has a bar missing (frequency 0), the frequency polygon... ", "options": {"A": "will have a point at zero", "B": "will skip that class", "C": "will not be affected", "D": "cannot be drawn"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "🔢 The area under a frequency polygon has no direct meaning. (True/False) ", "options": {"A": "True", "B": "False, it equals total frequency", "C": "False, it equals mean", "D": "False, it equals median"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "📐 For data: Intervals 5-15, 15-25, 25-35; Freq 6, 0, 10. What is the frequency at class mark 20? ", "options": {"A": "6", "B": "0", "C": "10", "D": "8"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "hard", "question": "📈 If the frequency polygon is a symmetric curve, the distribution is... ", "options": {"A": "skewed", "B": "uniform", "C": "symmetric", "D": "bimodal"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "hard", "question": "🎯 To draw a frequency polygon from a given histogram, you need to find... ", "options": {"A": "class boundaries and frequencies", "B": "class marks and frequencies", "C": "cumulative frequencies", "D": "upper limits only"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "hard", "question": "📊 For a histogram with class intervals 0-10, 10-30, 30-40, the width of the second bar is... ", "options": {"A": "10", "B": "20", "C": "30", "D": "40"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "hard", "question": "🔍 If total frequency is 50 and area of histogram is 250 sq cm, what is the area representing frequency 10? ", "options": {"A": "10 sq cm", "B": "25 sq cm", "C": "50 sq cm", "D": "5 sq cm"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "hard", "question": "📈 A frequency polygon is drawn by joining points. If the line segment between two points is horizontal, it means... ", "options": {"A": "frequencies are equal", "B": "class marks are equal", "C": "frequencies are zero", "D": "an error"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "🎯 In a histogram, if all class widths are equal, which bar represents the mode? ", "options": {"A": "The widest bar", "B": "The bar with greatest area", "C": "The bar with greatest height", "D": "The first bar"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "hard", "question": "📊 A frequency polygon can be smoothed to form a frequency curve. (True/False) ", "options": {"A": "True", "B": "False", "C": "Only for small data", "D": "Only for qualitative data"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "✅ The main advantage of a frequency polygon over a histogram is... ", "options": {"A": "it is easier to draw", "B": "it allows comparison of multiple distributions clearly", "C": "it shows area", "D": "it works for qualitative data"}, "correct_answer": "B"}
  ]
}