A class of seven students has a mean test grade of 82. Six of the grades are 80, 82, 86, 90, 90 and 95. What is the seventh grade?

1. A mean of 82 across seven students means the grades total 7 times 82, which is 574 marks. 2. The six known grades add to 80 plus 82 plus 86 plus 90 plus 90 plus 95. 3. That sum is 523 marks. 4. The missing grade is 574 minus 523, which is 51 marks. 5. Answering 82 assumes the missing grade equals the mean, which would only hold if the other six averaged 82 as well. 6. Answering 74 follows from using a total of 597 marks, which no mean of 82 across seven students can give. _Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.3 Measures of the Center of the Data_