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: Identify the given information. The distribution is symmetric. The Interquartile Range (IQR) is 10. The Median is 10. Step 2: Recall the properties of a symmetric distribution. For a symmetric distribution, the median is exactly halfway between the first quartile (Q1) and the third quartile (Q3). This means the distance from Q1 to the median is equal to the distance from the median to Q3. Mathematically, this can be expressed as: Median - Q1 = Q3 - Median The Interquartile Range (IQR) is defined as Q3 - Q1. For a symmetric distribution, the distance from Q1 to the median is half of the IQR: Median - Q1 = IQR2 Step 3: Substitute the given values into the formula. We are given IQR = 10 and Median = 10. 10 - Q1 = (10)/(2) 10 - Q1 = 5 Step 4: Solve for Q1. Q1 = 10 - 5 Q1 = 5 The First Quartile (Q1) is 5. This corresponds to the first option provided. The final answer is 5. 3 done, 2 left today. You're making progress.