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
Right Art, let's go. The given set of numbers is 2, 5, 4, 8, 3, 6, x, 9, 5, 4, 7. The mode is given as 5. a) To find the value of x: Step 1: Count the frequency of each number in the given set. The numbers are 2, 5, 4, 8, 3, 6, x, 9, 5, 4, 7. Frequencies: 2: 1 3: 1 4: 2 5: 2 6: 1 7: 1 8: 1 9: 1 Step 2: Determine x based on the mode. Since the mode is 5, it must be the number that appears most frequently. Currently, 4 and 5 both appear twice. For 5 to be the unique mode, x must be 5. x = 5 The value of x is 5. b) To find the median: Step 1: Substitute x=5 into the set and arrange the numbers in ascending order. The set becomes 2, 5, 4, 8, 3, 6, 5, 9, 5, 4, 7. Sorted set: 2, 3, 4, 4, 5, 5, 5, 6, 7, 8, 9. Step 2: Find the total number of data points (n) and the median position. There are 11 numbers, so n=11. The median is the ((n+1)/(2))-th term. Median position = (11+1)/(2) = (12)/(2) = 6^th Step 3: Identify the median from the sorted set. The 6^th term in the sorted set is 5. The median is 5. c) To find the lower and upper quartiles: Step 1: Use the sorted data and the median. Sorted data: 2, 3, 4, 4, 5, 5, 5, 6, 7, 8, 9. (Median is underlined) Step 2: Find the lower quartile (Q_1). Q_1 is the median of the lower half of the data (excluding the median itself for an odd n). Lower half: 2, 3, 4, 4, 5. There are 5 terms. Q_1 position = (5+1)/(2) = 3^rd The 3^rd term in the lower half is 4. So, Q_1 = 4. Step 3: Find the upper quartile (Q_3). Q_3 is the median of the upper half of the data (excluding the median itself). Upper half: 5, 6, 7, 8, 9. There are 5 terms. Q_3 position = (5+1)/(2) = 3^rd The 3^rd term in the upper half is 7. So, Q_3 = 7. The lower quartile is 4 and the upper quartile is 7. d) To find the interquartile range (IQR): Step 1: Use the calculated lower and upper quartiles. Q_1 = 4 and Q_3 = 7. Step 2: Calculate the IQR. IQR = Q_3 - Q_1 IQR = 7 - 4 = 3 The interquartile range is 3. Send me the next one 📸