Grade 9 · Math · Statistics
Sort first, then take the median
10 questions on mean and median, with a sorting space on each
أ. عمر الشريف
مدرسة أ
A short quiz written from students' wrong answers rather than from the book's examples. Every wrong option in it is an answer a student actually gave.
This page is exactly what a teacher's published work will look like. Only the teacher is not real yet.
What the student does
- 1
Meet an unsorted list
Every question hands over the numbers in a random order, not sorted the way the book prints them.
- 2
Sort it before answering
Every question has a space to rewrite the list in order, so sorting is a written step and not one done in the head.
- 3
Choose, and find out at once
A wrong option does not come back as the word «wrong». It comes back as a sentence naming what they calculated instead of what was asked.
- 4
Compare the two on one list
The last two questions use one and the same list, and it holds a single outlier that moves one measure and leaves the other alone.
What's inside
- Ten questions whose wrong options are taken from real student answers
- A sorting space on every question for rewriting the list
- Two lists, one with an odd count of values and one with an even count
- Immediate marking that explains the wrong option instead of just flagging it
Outcomes
Calculates the mean of an eight-value list and writes it to one decimal place.
Sorts an unsorted list in ascending order and then takes the median from it.
Finds the median of an even-length list by averaging the two middle values.
Explains why a single outlier moves the mean and leaves the median where it was.
What the teacher focused on
The median mistakes are not arithmetic. They take the value sitting in the middle of the line as printed, and it never occurs to them that the line needs sorting first.
Teaching strategies
- Every wrong option comes out of a student's notebook
- Sorting is a written step, never a mental one
- The outlier gets compared on one and the same list
He wrote the wrong options from answers collected over years rather than generating numbers near the right one, because a randomly close number gets ruled out by guessing alone, while an answer a student reached by a wrong method looks entirely correct to anyone thinking the same way. And he refused to print the lists in order, because the book prints them in order and the exam does not.
Questions from inside it
- 1The numbers: 7, 3, 9, 4, 12, 5, 8. What is the median?
- 2Six students' marks: 15, 18, 11, 20, 14, 16. What is the median?
- 3Seven players' ages: 13, 13, 14, 14, 15, 15, 40. The mean is 17.7 and the median is 14. Which one describes the team more truthfully, and why?
Curriculum
- Grade
- Grade 9
- Subject
- Math
- Unit
- Statistics
- Taught in
- Jordan
Where this lesson sits in the curriculum
The same lesson appears in these countries' curricula. One page, five paths to it.
When to use it
The explanation
The mean is the sum of the values divided by how many there are, so every value has a share in it, and that is why one extreme value drags it. The median is the value in the middle once the values are put in ascending order, so it does not care how large the largest value is, only how many values sit above it and how many below. When the count is even there is no single middle value, so you take the mean of the two in the middle. The load-bearing words in the definition are «once sorted», and they are the first words to go missing.
Common mistakes it catches
The median is the middle of the values, not the middle of the line. Make sorting a written line in the notebook: 3, 4, 5, 7, 8, 9, 12. The 7 is then simply there, with no calculation and no rule.
The count is even, so the middle is not a value but a place between two values. The median is the mean of 15 and 16, which is 15.5, and a median that appears nowhere in the list is perfectly normal.
Ask for both on the same list, inside the same question. When 17.7 and 14 come out of one set of seven ages, the difference becomes something they saw rather than something they memorised.