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
Step 1: Calculate the incorrect sum of observations. Given: Number of observations (n) = 100 Incorrect mean (X_incorrect) = 50 The formula for the mean is X = ( X)/(n). So, the incorrect sum of observations ( X_incorrect) can be calculated as: X_incorrect = X_incorrect × n X_incorrect = 50 × 100 X_incorrect = 5000 Step 2: Adjust the sum of observations. The two observations wrongly taken were 32 and 15. The correct observations should have been 82 and 51. To find the correct sum ( X_correct), subtract the incorrect values and add the correct values to the incorrect sum: X_correct = X_incorrect - (wrongly taken values) + (correct values) X_correct = 5000 - (32 + 15) + (82 + 51) X_correct = 5000 - 47 + 133 X_correct = 4953 + 133 X_correct = 5086 Step 3: Calculate the correct mean. Using the correct sum and the number of observations: X_correct = X_correctn X_correct = (5086)/(100) X_correct = 50.86 The correct mean is 50.86. Last free one today — make it count tomorrow, or type /upgrade for unlimited.