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.
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Here are the solutions for questions 5, 6, and 7 based on the provided frequency distribution table. The table shows: Number of Chairs (x): 1, 2, 3, 4, 5, 6, 7 Frequency (f): 2, 7, 5, 4, 9, 7, 6 The total number of rooms (total frequency) is f = 2+7+5+4+9+7+6 = 40. Question 5: Find the mean. Step 1: Calculate the product of each number of chairs (x) and its frequency (f), i.e., fx. 1 × 2 = 2 2 × 7 = 14 3 × 5 = 15 4 × 4 = 16 5 × 9 = 45 6 × 7 = 42 7 × 6 = 42 Step 2: Calculate the sum of fx values. fx = 2 + 14 + 15 + 16 + 45 + 42 + 42 = 176 Step 3: Calculate the mean using the formula x = ( fx)/( f). x = (176)/(40) x = 4.4 The mean is C. 4.4. Question 6: Find the mode. Step 1: Identify the highest frequency in the table. The frequencies are 2, 7, 5, 4, 9, 7, 6. The highest frequency is 9. Step 2: Determine the number of chairs (x) corresponding to the highest frequency. The number of chairs corresponding to the frequency 9 is 5. The mode is D. 5. Question 7: Find the median. Step 1: Determine the total number of data points (N). N = f = 40. Step 2: Find the position of the median. Since N is an even number, the median is the average of the ((N)/(2))-th and ((N)/(2) + 1)-th values. (N)/(2) = (40)/(2) = 20. So, we need the 20th and 21st values. Step 3: Calculate the cumulative frequencies to locate the median values. Number of Chairs (x) | Frequency (f) | Cumulative Frequency (cf) ---------------------|---------------|-------------------------- 1 | 2 | 2 2 | 7 | 2+7=9 3 | 5 | 9+5=14 4 | 4 | 14+4=18 5 | 9 | 18+9=27 6 | 7 | 27+7=34 7 | 6 | 34+6=40 Step 4: Identify the 20th and 21st values. From the cumulative frequency table: The 1st to 2nd values are 1. The 3rd to 9th values are 2. The 10th to 14th values are 3. The 15th to 18th values are 4. The 19th to 27th values are 5. Therefore, both the 20th value and the 21st value are 5. Step 5: Calculate the median. Median = 20th value + 21st value2 = (5 + 5)/(2) = (10)/(2) = 5 The median is 5. (Note: The visible options A. 6.5 and B. 9.0 do not include 5.0, which is the calculated median.) What's next?