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've done a good job starting the process, James, but there are a few corrections needed in your ordered list and the subsequent calculations. Let's go through it step by step. Question #1) Calculate the mean, median, mode, and range for the following sales data: 1700; 2200; 2400; 2900; 1800; 3700; 1200; 2300; 600; 1600; 2000; 3900; 1100; 1700; 2900; 2900; 2900. Step 1: Correct the ordered data. The original dataset has one 2200, one 2300, one 2400, and four 2900s. Your ordered list had some values duplicated or missed. Here is the correct ordered list: 600, 1100, 1200, 1600, 1700, 1700, 1800, 2000, 2200, 2300, 2400, 2900, 2900, 2900, 2900, 3700, 3900. There are n=17 data points. Step 2: Calculate the mean. First, let's sum the values from the correct ordered list: x = 600+1100+1200+1600+1700+1700+1800+2000+2200+2300+2400+2900+2900+2900+2900+3700+3900 = 37600 Now, calculate the mean: Mean = ( x)/(n) = (37600)/(17) ≈ 2211.7647 Rounding to two decimal places: The mean is \2211.76. Step 3: Interpret the mean. The mean of 2211.76 indicates that the average sales value across all 17 data points is approximately 2211.76. It represents the central tendency of the sales data. Step 4: Calculate the median. Since there are 17 data points (an odd number), the median is the ((n+1)/2)-th value in the ordered list. Median position = (17+1)/(2) = 9-th value Counting to the 9th value in the correct ordered list: 600, 1100, 1200, 1600, 1700, 1700, 1800, 2000, 2200, 2300, 2400, 2900, 2900, 2900, 2900, 3700, 3900. The 9th value is 2200. The median is \2200. Step 5: Interpret the median. The median of 2200 means that half of the sales values are below 2200 and half are above 2200. It is the middle value of the dataset when arranged in order. Step 6: Calculate the mode. The mode is the value that appears most frequently in the dataset. In the correct ordered list, the value 2900 appears 4 times, which is more than any other value. The mode is \2900. Step 7: Interpret the mode. The mode of 2900 indicates that 2900 is the most common sales value in this dataset. Step 8: Calculate the range. The range is the difference between the maximum and minimum values in the dataset. Range = Maximum Value - Minimum Value = \3900 - \600 = \3300 The range is \3300. 3 done, 2 left today. You're making progress.