Ping chooses four numbers - OCR - GCSE Maths - Question 19 - 2018 - Paper 1

The mean is calculated as:

$ext{Mean} = \frac{a + b + c + d}{4}$

Given that the mean is 11, we can set up the equation:

$a + b + c + d = 4 \times 11 = 44$

Since the mode is 8, at least two of the numbers must be 8. Therefore, let’s assume:

• a = 8
• b = 8 This gives us:

$c + d = 44 - 16 = 28$

The range is defined as:

$ext{Range} = d - a$

Given that the range is 7 and a = 8, we can express d as:

$d - 8 = 7 \implies d = 15$

Substituting into the equation: $c + 15 = 28 \implies c = 13$

Thus, the four numbers chosen by Ping are:

$a = 8, b = 8, c = 13, d = 15$.