Ping chooses four numbers - OCR - GCSE Maths - Question 1 - 2018 - Paper 1

To find the four numbers, we need to satisfy the following conditions:

1. Mode: The mode is 8, which means 8 must appear more frequently than the other numbers. Thus, at least two of the four numbers must be 8.

2. Mean: The mean is 11, therefore the total sum of the four numbers must be:

   $ext{Total} = ext{Mean} \times ext{Number of values} = 11 \times 4 = 44$

3. Range: The range is 7, so the difference between the largest and smallest number must be 7.

Given these conditions, let's denote the four numbers as: 8, 8, x, and y, where x and y are the other two numbers. We now have:

• From the mean:

  $8 + 8 + x + y = 44$

  This simplifies to:

  $x + y = 28$

• There is also the range condition:

  $y - 8 = 7 \Rightarrow y = 15$

Substituting y into the equation for the mean, we get:

$x + 15 = 28 \Rightarrow x = 13$

Thus, the four numbers are: 8, 8, 13, and 15.