This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's the solution to the statistics problem. a) i) Determine the value of X. Step 1: Sum the given frequencies. The total number of students is 100. The frequencies are 4, 6, 10, 14, X, 24, 14, 6. Sum of known frequencies = 4 + 6 + 10 + 14 + 24 + 14 + 6 = 78. Step 2: Calculate X. The sum of all frequencies must equal the total number of students. 78 + X = 100 X = 100 - 78 X = 22 The value of X is 22. ii) The modal class. Step 1: Identify the highest frequency. The frequencies are 4, 6, 10, 14, 22 (for X), 24, 14, 6. The highest frequency is 24. Step 2: Determine the class corresponding to the highest frequency. The class interval corresponding to the frequency 24 is 55-59. The modal class is 55-59. b) Calculate the mean. Step 1: Find the midpoint (x) for each class interval. • 30-34: x = (30+34)/(2) = 32 • 35-39: x = (35+39)/(2) = 37 • 40-44: x = (40+44)/(2) = 42 • 45-49: x = (45+49)/(2) = 47 • 50-54: x = (50+54)/(2) = 52 • 55-59: x = (55+59)/(2) = 57 • 60-64: x = (60+64)/(2) = 62 • 65-69: x = (65+69)/(2) = 67 Step 2: Calculate the product of frequency (f) and midpoint (x) for each class (fx). • 4 × 32 = 128 • 6 × 37 = 222 • 10 × 42 = 420 • 14 × 47 = 658 • 22 × 52 = 1144 • 24 × 57 = 1368 • 14 × 62 = 868 • 6 × 67 = 402 Step 3: Sum the fx values ( fx). fx = 128 + 222 + 420 + 658 + 1144 + 1368 + 868 + 402 = 5210 Step 4: Calculate the mean using the formula x = ( fx)/( f). The total frequency f = 100. x = (5210)/(100) x = 52.1 The mean is 52.1. Last free one today — make it count tomorrow, or type /upgrade for unlimited.