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
You're on a roll — Here are the solutions for the data set: 3, 4, 5, 7, 8, 9, 10, 11, 6, 13, 15, 21, 3. First, let's sort the data set in ascending order: 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 21. The total number of data points is n = 13. a) Determine the average of the data set. Step 1: Sum all the values in the data set. Sum = 3 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 13 + 15 + 21 = 115 Step 2: Divide the sum by the total number of data points. Average = Sumn = (115)/(13) ≈ 8.85 The average of the data set is 8.85. b) Determine the modal value of the data. Step 1: Identify the value that appears most frequently in the data set. In the sorted data set (3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 21), the number 3 appears twice, while all other numbers appear only once. The modal value is 3. c) Determine the Probability of choosing a value that is less than 10. Your answer should be in percentages. Step 1: Count the number of values in the data set that are less than 10. The values less than 10 are: 3, 3, 4, 5, 6, 7, 8, 9. There are 8 such values. Step 2: Calculate the probability as a fraction. Probability = Number of values less than 10Total number of values = (8)/(13) Step 3: Convert the probability to a percentage. Percentage = (8)/(13) × 100\% ≈ 61.54\% The probability of choosing a value less than 10 is 61.54\%. d) Determine the Middle Value of the data set. Step 1: The data set is already sorted: 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 21. The number of data points is n = 13. Step 2: Find the position of the middle value (median) using the formula (n+1)/(2). Median position = (13+1)/(2) = (14)/(2) = 7^th The 7^th value in the sorted data set is 8. The middle value of the data set is 8. e) Determine the gap between the highest value and the lowest value. Step 1: Identify the highest and lowest values in the data set. Highest value = 21 Lowest value = 3 Step 2: Calculate the difference between the highest and lowest values. Gap (Range) = Highest value - Lowest value = 21 - 3 = 18 The gap between the highest and lowest value is 18. Send me the next one 📸