Question 4 of 15intermediate🔧 ApplyNumerical2 marks

The mean of the numbers 8, 13, 10, 4, 5, 20, y, 10 is 10.375. Find the value of y.

Correct Answer

Given: Numbers: 8, 13, 10, 4, 5, 20, y, 10; Mean = 10.375 Formula: Mean = Sum of values / Number of values Substitution: (8 + 13 + 10 + 4 + 5 + 20 + y + 10) / 8 = 10.375 Calculation: Sum of known values = 8 + 13 + 10 + 4 + 5 + 20 + 10 = 70 (70 + y) / 8 = 10.375 70 + y = 10.375×810.375 \times 8 70 + y = 83 y = 83 - 70 = 13 Answer: The value of y is 13.

Exercise: Figure it Out (Section 1) | Q: 7 | (Page Page 13)
For More Understanding

Explanation

The chapter demonstrates finding unknown values when the mean is known. Using the formula: Mean = Sum of values / Number of values, we can solve for the unknown.

Solution Steps

  1. Step 1: Set up the equation using the mean formula: (8 + 13 + 10 + 4 + 5 + 20 + y + 10)/8 = 10.375

  2. Step 2: Sum the known values: 8 + 13 + 10 + 4 + 5 + 20 + 10 = 70

  3. Step 3: Write: (70 + y)/8 = 10.375

  4. Step 4: Multiply both sides by 8: 70 + y = 83

  5. Step 5: Solve for y: y = 83 - 70 = 13

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