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: Count the number of data points (n). The given data points are: 20, 20, 30, 30, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40. There are n = 33 data points. Step 2: Calculate the Mean. The mean is the sum of all data points divided by the number of data points. Sum = (2 × 20) + (2 × 30) + (29 × 40) Sum = 40 + 60 + 1160 Sum = 1260 Mean = Sumn = (1260)/(33) Mean ≈ 38.1818... Rounding to two decimal places: Mean ≈ 38.18 Step 3: Calculate the Median. The median is the middle value of an ordered data set. Since the data is already ordered and n=33 (an odd number), the median is the value at the (n+1)/(2)-th position. Position = (33+1)/(2) = (34)/(2) = 17 The 17th value in the ordered data set is 40. Median = 40 Step 4: Calculate the Mode. The mode is the value that appears most frequently in the data set. • The value 20 appears 2 times. • The value 30 appears 2 times. • The value 40 appears 29 times. The value 40 appears most frequently. Mode = 40 That's 2 down. 3 left today — send the next one.