In this lesson:
By the end of this lesson, you will:
The dot plot below shows the heights of 25 sixth graders — the same data from last lesson.
A friend texts: "How tall are kids in your class?"
You can reply with at most two numbers — one for what's typical, one for how spread out.
What would you send?
Five students have 4, 7, 5, 3, 6 stickers — shown as cube stacks.
You want to give everyone the same number of stickers without adding or removing any.
How many stickers would each student get?
Try to figure it out before the next slide.
The mean of 4, 7, 5, 3, 6 is 5.
Four quiz scores: 7, 8, 9, 10
Step 1: Add all values
Step 2: Divide by the count
Mean = 8.5 — non-integer, though every score is a whole number.
The 25 sixth-grader heights add up to 1455 inches.
Your turn: Complete the calculation.
Calculate, then advance for the answer.
Find the mean of 3, 6, 9.
Think it through, then advance.
The mean and median both answer "what's typical?" — but differently.
Key difference: the median cares about position, not the size of each value.
Five values as written, not ordered:
7, 3, 8, 5, 5
Which is the "middle" value?
Pick before advancing.
Data (already ordered): 3, 5, 5, 7, 8
Data (already ordered): 3, 4, 5, 7, 8, 10
Note: 6 does not appear in the data set — and that's fine.
52, 54, 54, 55, 55, 55, 56, 56, 56, 56, 57, 57, 57, 58, 58, 58, 59, 59, 60, 60, 61, 62, 63, 63, 65
The gap is not a mistake — it reflects the data's shape.
Find the median of: 2, 5, 7, 11, 14
Is the count odd or even? Sort first. Then identify the middle value.
Data: 2, 5, 7, 11, 14
Neither mean nor median tells you how spread out the data is.
You have two measures of center: mean and median.
Two data sets can share both the mean and median — yet look completely different.
Next question: how do we measure how spread out the data is?
A description with only center: "typical height is 58.2 inches." A description with both: "typical height is 58.2 inches; heights vary by 13 inches."
Range ignores every value between the extremes.
Coming in 6.SP.B.5: IQR and MAD use more data, making them more reliable.
Find the mean, median, and range for:
Write your work: order the data, then compute each measure.
A student computed the median of 7, 3, 8, 5, 5 as:
"The 3rd value is 8. Median = 8."
What is wrong? What is the correct median?
Identify the error, write the correction, then advance.
The student skipped sorting — the required first step.
Unordered: 7, 3, 8, 5, 5 → 3rd item = 8 ✗
Ordered: 3, 5, 5, 7, 8 → 3rd value = 5 ✓
Median = 5, not 8. Sort first, every time.
Compare the two data sets:
Work through all three parts, then advance.
Two-number summary reveals what mean alone hides.
For the data set: 4, 9, 6, 2, 9, 6
Find each of the following — show all work.
No hints. Demonstrate all three on your own.
Ordered: 2, 4, 6, 6, 9, 9
✓ Mean = total ÷ count — the leveling value; uses every data point
✓ Median = middle of the ordered list; unaffected by extremes
✓ Range = max − min — the simplest measure of variation
✓ Center + variation together form a basic two-number summary
Sort first — median from an unordered list is wrong
Mean ≠ (max + min) ÷ 2 — use all values, not just two
Mean-median gap = information, not a mistake
Range is limited — one outlier inflates it
In 6.SP.B.4: box plots show median and range visually in one diagram.
In 6.SP.B.5: IQR and MAD — variation measures using more data than range, helping you choose between mean and median.