Statistics

65

Step 1: Use the mean formula to find total sum: Mean = Sum ÷ Number of observations, so Sum = Mean × Number of observations. Step 2: Calculate total sum of 5 numbers: Sum = 20 × 5 = 100. Step 3: One number is given as 35. Step 4: Sum of remaining 4 numbers = Total sum - Given number = 100 - 35 = 65. Therefore, the sum of the remaining 4 numbers is 65.

14

Step 1: Check if data is arranged in order - yes, it's in ascending order: 4, 8, 12, 16, 20, 24. Step 2: Count the observations: n = 6 (even number). Step 3: For even n, median is the average of (n/2)th and (n/2 + 1)th values. Here, n/2 = 3, so we need 3rd and 4th values. Step 4: 3rd value = 12, 4th value = 16. Median = (12 + 16) ÷ 2 = 28 ÷ 2 = 14.

8

Step 1: Write the mean formula: Mean = Sum of observations ÷ Number of observations. Step 2: Substitute known values: 10 = (7 + 9 + 11 + x + 15) ÷ 5. Step 3: Simplify: 10 = (42 + x) ÷ 5. Step 4: Multiply both sides by 5: 50 = 42 + x. Step 5: Solve for x: x = 50 - 42 = 8. Therefore, x = 8.

23

Step 1: Identify the maximum value in the data: Looking at 15, 22, 8, 19, 31, 12, the maximum is 31. Step 2: Identify the minimum value in the data: The minimum is 8. Step 3: Apply the range formula: Range = Maximum value - Minimum value. Step 4: Calculate: Range = 31 - 8 = 23. Therefore, the range is 23.