How to calculate the median when each value from the data is increased by 10?

Question

Given that a collection of scores on a quiz leads to a mean of 40, a median of 38, and a mode of 36. If we added 10 points to each score what would be the new median?

Answer 1

Originally you have a set of quiz grades: {$q_1, q_2, q_3, ..., q_n$}, then 10 is added to each quiz grade to get a new set: {$q_1+10, q_2+10, q_3+10, ..., q_n+10$}

If the mean was originally 40, the new mean will be 50. This can be seen since: $$\frac{\sum_{i=0}^n q_n+10}{n} =\frac{\sum_{i=0}^n q_n}{n} + \frac{\sum_{i=0}^n 10}{n} = Original\ Mean\ + \frac{10n}{n} = original\ mean\ + 10$$ If the median was originally 38, the new median will be 48. The median is the middle number in a set of numbers, therefore if all the numbers are increased by 10, the middle number will be its original value + 10.

If the mode was originally 36, the new mode will be 46. The mode is the number which appears most often in the set of data, so all the numbers in the set are increased by 10, the mode will be its old value + 10.