Question 10 of 15intermediate🔧 ApplyShort Answer3 marks

Fill in the blanks such that the mean of the collection is 6.5: 3, 11, ___, ___, 15, 6. How many possibilities exist if only counting numbers are allowed?

Correct Answer

Given: 6 values with mean 6.5

Formula: Sum = Mean × Number of values

Calculation: Total sum = 6.5×66.5 \times 6 = 39 Sum of known values = 3 + 11 + 15 + 6 = 35 Sum of two missing values = 39 - 35 = 4 Counting number pairs that sum to 4: (1, 3), (2, 2), (3, 1)

Answer: There are 3 possibilities.

Exercise: Figure it Out (Section 3) | Q: 4 | (Page Page 25)
For More Understanding

Explanation

The chapter demonstrates finding unknown values when the mean is known. Use the formula: Sum = Mean × Number of values, then find what the missing values must sum to.

Solution Steps

  1. Step 1: Calculate required total sum: Mean × n = 6.5×66.5 \times 6 = 39

  2. Step 2: Sum of known values: 3 + 11 + 15 + 6 = 35

  3. Step 3: Sum of two missing values: 39 - 35 = 4

  4. Step 4: Find counting number pairs that sum to 4: (1, 3), (2, 2), (3, 1)

  5. Step 5: Total possibilities = 3

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