{
  "title": "Measures of Central Tendency - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Which is NOT a measure of central tendency? 📊", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "Range"}, "correct_answer": "D"},
    {"id": 2, "difficulty": "easy", "question": "The most frequent value is called? 🔝", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "Midrange"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "The middle value when data is arranged is? 📏", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "Average"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "Sum of all values divided by count gives? ➗", "options": {"A": "Median", "B": "Mode", "C": "Mean", "D": "Range"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "For data 2,3,5,7,7,8,10, mode is? 🔢", "options": {"A": "5", "B": "7", "C": "8", "D": "10"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "For data 4,6,8,10,12, median is? 📍", "options": {"A": "6", "B": "8", "C": "9", "D": "10"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "Mean of 5 numbers is 20. Their sum is? ➕", "options": {"A": "4", "B": "20", "C": "100", "D": "120"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "Which is affected by extreme values? 📈", "options": {"A": "Median", "B": "Mode", "C": "Mean", "D": "All"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "For symmetric distribution, mean = median = ? ⚖️", "options": {"A": "Mode", "B": "Range", "C": "Variance", "D": "SD"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Data can have more than one? 🤔", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "All"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "For categorical data, best measure is? 🏷️", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "Range"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "The balance point of data is? ⚖️", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "Midpoint"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "For data with outliers, best measure is? 🎯", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "All"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Mean of 10,20,30 is? 🧮", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "If each value is increased by 5, mean increases by? ➕", "options": {"A": "5", "B": "10", "C": "Same", "D": "25"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Median of 3,1,7,5,9 after arranging? 📊", "options": {"A": "3", "B": "5", "C": "7", "D": "9"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Mode of 2,2,3,4,4,4,5 is? 🔝", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "If mean=median=mode, distribution is? 📈", "options": {"A": "Skewed", "B": "Symmetric", "C": "Bimodal", "D": "Uniform"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "Which always exists in data? ✅", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "All"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "For open-ended classes, we can find? 📊", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "All"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "Mean of first n natural numbers is? 🔢", "options": {"A": "n/2", "B": "(n+1)/2", "C": "n(n+1)/2", "D": "n²/2"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "If mean of 5 numbers is 18, and four are 15,18,20,21, find fifth. 🧮", "options": {"A": "16", "B": "17", "C": "18", "D": "19"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "For data: 5,7,8,x,12,14 with mean 10, find x. ➕", "options": {"A": "10", "B": "12", "C": "14", "D": "16"}, "correct_answer": "C"},
    {"id": 24, "difficulty": "medium", "question": "Median of 25 numbers is 15th value when arranged. If 16th value is 20, median is? 📏", "options": {"A": "15", "B": "17.5", "C": "20", "D": "Average of 15th & 16th"}, "correct_answer": "D"},
    {"id": 25, "difficulty": "medium", "question": "Mode of 3,5,5,7,7,7,9,9,11 is? 🔝", "options": {"A": "5", "B": "7", "C": "9", "D": "5 & 7"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "If each observation is multiplied by 3, new mean = ? ✖️", "options": {"A": "Old mean", "B": "3 × old mean", "C": "Old mean/3", "D": "Old mean + 3"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "Mean of a,b,c is m. Mean of a,b,c,d is? 🧮", "options": {"A": "m", "B": "m+d/4", "C": "(3m+d)/4", "D": "m+d"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "For data with frequencies: x:2,3,4; f:5,8,7. Mean? 📊", "options": {"A": "3", "B": "3.1", "C": "3.2", "D": "3.3"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "If mean=50, median=48, mode=? (empirical) 🔗", "options": {"A": "44", "B": "46", "C": "52", "D": "54"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Which is true for positively skewed data? 📈", "options": {"A": "Mean>Median>Mode", "B": "Mode>Median>Mean", "C": "Median>Mean>Mode", "D": "Mean=Median=Mode"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Sum of deviations from mean is always? ➖", "options": {"A": "0", "B": "1", "C": "Positive", "D": "Negative"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "If mode=25, mean=30, median=? 🔗", "options": {"A": "27.5", "B": "28.33", "C": "29", "D": "31.67"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "For data: 10,12,14,16,18,20, median is average of? 📍", "options": {"A": "12 & 14", "B": "14 & 16", "C": "16 & 18", "D": "18 & 20"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "Mean of 100 numbers is 50. If each is increased by 10, new mean? ➕", "options": {"A": "50", "B": "60", "C": "70", "D": "100"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "For grouped data, we use class mark to compute? 📊", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "All"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "If sum of 15 numbers is 300, their mean is? ➗", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "Data: 3,5,7,9,11. If each is doubled, new median? ✖️", "options": {"A": "7", "B": "10", "C": "14", "D": "18"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "For continuous data, mode is in class with? 📊", "options": {"A": "Lowest frequency", "B": "Highest frequency", "C": "Middle frequency", "D": "Any frequency"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "If mean of a,a+2,a+4,a+6,a+8 is 12, find a. 🧮", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Which is not a positional average? 📍", "options": {"A": "Median", "B": "Mode", "C": "Mean", "D": "Quartile"}, "correct_answer": "C"},

    {"id": 41, "difficulty": "hard", "question": "Mean of 1²,2²,3²,...,n² is? 🔢", "options": {"A": "n(n+1)/2", "B": "(n+1)(2n+1)/6", "C": "n(n+1)(2n+1)/6", "D": "n²/3"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "If mean of 10 numbers is 20, and each is multiplied by 2 then increased by 3, new mean? 🔄", "options": {"A": "40", "B": "43", "C": "46", "D": "50"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "hard", "question": "For data with mean 25, if each xᵢ is replaced by (xᵢ-10)/5, new mean? 🧮", "options": {"A": "3", "B": "5", "C": "10", "D": "15"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "Mode of data: 10,12,12,15,15,15,18,20,20,20,25 is? 🔝", "options": {"A": "15", "B": "20", "C": "15 & 20", "D": "No mode"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "hard", "question": "If mean of a,b,c is m, mean of pa+q, pb+q, pc+q is? 🧮", "options": {"A": "pm+q", "B": "pm", "C": "qm", "D": "p+qm"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "Median of first 50 even numbers is? 🔢", "options": {"A": "50", "B": "51", "C": "52", "D": "100"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "hard", "question": "For data with mean 40 and median 38, if each value is increased by 10%, new median? 📈", "options": {"A": "38", "B": "41.8", "C": "44", "D": "48"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "hard", "question": "If sum of squares of 5 numbers is 500 and mean is 10, variance? 📊", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "For grouped data with open ends, which is most reliable? 🎯", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "All"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "hard", "question": "If mode=60, mean=65, coefficient of skewness? 📐", "options": {"A": "0.5", "B": "-0.5", "C": "1", "D": "-1"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "hard", "question": "For data: x:1-10,11-20,21-30; f:5,?,15. If mean=18, missing f? 🧮", "options": {"A": "10", "B": "12", "C": "15", "D": "20"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "If each value in data set is increased by k, which changes? ➕", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "All"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "hard", "question": "For negatively skewed data, which is smallest? 📉", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "All equal"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "If mean of n numbers is M, and one number x is replaced by y, new mean? 🔄", "options": {"A": "M + (y-x)/n", "B": "M + (x-y)/n", "C": "M + (y-x)", "D": "M + (x-y)"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "For data with two modes 15 & 25, distribution is? 📊", "options": {"A": "Unimodal", "B": "Bimodal", "C": "Trimodal", "D": "No mode"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "hard", "question": "If sum of deviations from 4 is 20 and from 6 is -10, mean? 🧮", "options": {"A": "4.5", "B": "5", "C": "5.5", "D": "6"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "hard", "question": "Median of data: 12,15,18,x+2,x+4,30,32,35 is 24. Find x. 📏", "options": {"A": "20", "B": "21", "C": "22", "D": "23"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "hard", "question": "If mean of a,b,c,d,e is 10, mean of a,b,c,d,e,f is 11, f=? ➕", "options": {"A": "11", "B": "14", "C": "16", "D": "18"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "hard", "question": "For continuous data, empirical relation is approximate because? 🤔", "options": {"A": "Grouping error", "B": "Assumes symmetry", "C": "Uses class marks", "D": "All"}, "correct_answer": "D"},
    {"id": 60, "difficulty": "hard", "question": "If each frequency in grouped data is doubled, mean? ✖️", "options": {"A": "Doubles", "B": "Halves", "C": "Same", "D": "Cannot say"}, "correct_answer": "C"}
  ]
}