Jenny played four games of golf - OCR - GCSE Maths - Question 18 - 2017 - Paper 1

The modal score is defined as the number that appears most frequently in a set. Since the modal score is 76, at least two of her four scores must be 76.

The range of scores is defined as the difference between the highest and lowest scores. Given that the range is 10, if we denote the highest score as H and the lowest score as L, we have:

$H - L = 10$.

Given the conditions, let us assume the scores are:

• Two scores of 76 (modal score)
• One score of L (minimum score)
• One score of H (maximum score)

This implies:

$76 + 76 + L + H = 300$

Substituting for H:

$76 + 76 + L + (L + 10) = 300$

This simplifies to:

$152 + 2L + 10 = 300$ $2L = 300 - 162$ $2L = 138$ $L = 69$.

Following back, when H is found as:

$H = L + 10 = 69 + 10 = 79.$

Thus, the plausible scores are 69, 76, 76, and 79.