Mean, Median & Mode Grade 6 · 6.SP.B
Measure of Center

Mean

The "fair share" — what each value would be if everything were spread out equally.
➗
Definition

The mean is the average. Add all values, then divide by how many there are.

VISUAL

What does the mean look like?

Points per game → 2, 4, 6, 8, 10
2
G1
4
G2
6
G3
8
G4
10
G5
Mean = 6

The dashed line = the "leveling out" point. Imagine pouring all the bars into one pool and splitting evenly.

STEPS

Step by step

1
List All Values

Write out every number.

2, 4, 6, 8, 10
2
Add (Find the Sum)

Add every value together.

2+4+6+8+10 = 30
3
Count the Values

How many numbers are there?

5 values
4
Divide Sum ÷ Count

That's your mean!

30 ÷ 5 = 6 ← Mean!
GUIDED PRACTICE

Try it with support

PROBLEM 1
Books read last month: 3, 7, 5, 9, 1. What is the mean?
37591
Fill in the blanks
▶ Sum: 3+7+5+9+1 =
▶ Count: values
▶ Mean: ÷ =
Mean =
PROBLEM 2
Goals scored in 4 games: 2, 6, 4, 8. Find the mean.
2648
Show your work
▶ Sum =   Count =
▶ Mean = ÷ =
Mean =
PROBLEM 3
Temperatures (°F): 70, 75, 80, 65, 90, 85, 75. Find the mean. Round to the nearest tenth.
70758065908575
Mean =

Hint: Sum = 540. Divide by 7.

PROBLEM 4
Marcus ran these distances (miles) over 6 days: 3.5, 4, 2.5, 5, 3, 4. What was his mean daily distance?
3.542.5534
Mean =

Hint: Sum = 22. 22 ÷ 6 ≈ ?

PROBLEM 5
A store sold these many items each day last week: 42, 38, 55, 61, 44, 37, 49. What is the mean number of items sold per day?
42385561443749
Mean =

Hint: Sum = 326. Divide by 7. Round to nearest hundredth.

PROBLEM 6 — CHALLENGE
A student scored 82, 91, 78, and 85 on four tests. What score does she need on the 5th test to have a mean of 85?
5th score =

Think backwards: Mean × Count = Sum. What sum do you need? What's missing?

Measure of Center

Median

The middle value — once data is ordered smallest to largest.
🎯
Definition

The median is the middle number in an ordered set. With two middle numbers, find their mean.

VISUAL

Finding the middle

ODD count: 3, 7, 12, 15, 20 — click to sort
12320715
EVEN count: 4, 8, 10, 14 — two middle values
481014
STEPS

Step by step

1
Order Smallest → Largest

Rewrite all numbers in order.

9,3,7,1,5 → 1,3,5,7,9
2
Cross Off Both Ends

Remove the smallest and largest, keep going until 1 or 2 remain.

~~1~~, 3, 5, 7, ~~9~~
3
One Left = Median. Two Left = Average Them.
Median = 5
GUIDED PRACTICE

Try it with support

PROBLEM 1
Ages in a club: 11, 14, 12, 13, 10. Find the median.
1114121310
Fill in the steps
▶ Ordered: , 11, , 13,
▶ 5 values → odd → middle is the rd value
Median =
PROBLEM 2
Test scores: 88, 72, 95, 81, 77, 90. Find the median (even count!).
887295817790
Show your work
▶ Ordered: 72, 77, , , 90, 95
▶ Two middles: and → average:
Median =
PROBLEM 3
Plant heights (inches): 5, 12, 8, 3, 15, 9, 6. Find the median.
512831596
Median =

Order first: 3, 5, 6, ?, 9, 12, 15

PROBLEM 4
Time (minutes) to finish homework each night: 45, 30, 60, 25, 50, 40. Find the median.
453060255040
Median =

Ordered: 25, 30, 40, 45, 50, 60 → two middles are 40 and 45.

PROBLEM 5
Number of steps walked each day: 8200, 7500, 9100, 6800, 10400, 7500, 8800, 9300. Find the median.
820075009100680010400750088009300
Median =

8 values → even count. Order them, then average the 4th and 5th.

PROBLEM 6 — CHALLENGE
The median of five numbers is 14. Four of the numbers are 8, 11, 18, 22. What is the fifth number? (There may be more than one answer!)
One valid answer =

The 5th number, when inserted and ordered, must land in the middle as 14. Think: where could 14 go?

Measure of Center

Mode

The most popular value — shows up most often in the data.
⭐
Definition

The mode is the value that appears most frequently. A data set can have one mode, more than one, or no mode.

One Mode

1, 2, 3, 3, 3, 4, 5 → Mode = 3

Bimodal (Two Modes)

1, 2, 2, 3, 4, 4, 5 → Modes = 2 and 4

No Mode

1, 2, 3, 4, 5 → All appear once — no mode!

Works With Words!

Red, Green, Green, Green, Blue → Mode = Green

VISUAL

Dot plot — see the mode!

Favorite snacks chosen by 12 students:
Apple Chips Cookie Pretzel MODE ⭐

Chips has the tallest stack → Chips is the mode!

GUIDED PRACTICE

Try it with support

PROBLEM 1
Shoe sizes: 7, 8, 6, 8, 9, 8, 7, 6, 8. What is the mode?
786898768
Tally each value
▶ 6 appears times   7 appears times
▶ 8 appears times ← most!   9 appears time
Mode =
PROBLEM 2 — BIMODAL
Temperatures: 72, 75, 72, 80, 75, 68, 80. Find all modes.
72757280756880
PROBLEM 3
Push-ups: 15, 20, 15, 30, 20, 15, 25, 10. What is the mode?
1520153020152510
Mode =
PROBLEM 4
Number of siblings: 1, 0, 2, 3, 1, 2, 0, 1, 4, 1. What is the mode?
1023120141
Mode =
PROBLEM 5 — NO MODE
Quiz scores: 91, 83, 77, 95, 88. Does this data set have a mode?
9183779588
PROBLEM 6 — REAL WORLD
A clothing store sold these shirt sizes this week: M, L, S, L, XL, M, L, M, L, S, L. Which size should they order most for next week?

Count each size: S=2, M=3, L=5, XL=1. The mode tells you the most popular item!

🔬 Explore All Three

Enter any data set and see all three measures calculated step by step.

Mean
—
Median
—
Mode
—

Step-by-Step Breakdown

SCENARIO

Apply to a real situation

🏀

Basketball Season Stats

Marcus played 8 games: 12, 20, 8, 20, 15, 20, 10, 17 points.

MEAN

What was his mean points per game?

Sum = 122. 122 ÷ 8 = ?

MEDIAN

Ordered: 8, 10, 12, 15, 17, 20, 20, 20. Find the median.

Even count (8) → average 4th and 5th values: 15 and 17.

MODE

Which score appears most often?

THINK

The coach says "Marcus typically scores about 15 points." Which measure supports this claim?

Mean (15.25) ≈ 15. The mode (20) is his "go-to" game. The median (16) is close. Mean is what the coach likely used.

⚡ Rapid Fire Quiz

20 questions — mean, median, and mode. Pick the right answer. How many can you get?

Question 1 of 20
Score: 0/0

🗂️ Sort It Out

Drag each description or example into the correct bucket — Mean, Median, or Mode.

ROUND 1

Sort these descriptions

Drag each card into the correct column below.

MEAN
MEDIAN
MODE
ROUND 2

Sort these data set examples

Each card shows a data set and an answer. Sort by which measure of center was found.

MEAN
MEDIAN
MODE

🔍 Error Hunt

A student made a mistake in each problem below. Find the error and explain the correct method.

ERROR ANALYSIS #1 — MEAN

Data: 4, 6, 8, 10. A student wrote:

Step 1: Add all values: 4 + 6 + 8 + 10 = 28
Step 2: Divide by 3 (because the largest number is 10 and 10 − 7 = 3?)
Answer: Mean = 28 ÷ 3 ≈ 9.3

What mistake did the student make? What is the correct mean?

The student divided by 3 instead of 4. There are 4 values in the data set, so you must divide by 4. Correct mean: 28 ÷ 4 = 7.
ERROR ANALYSIS #2 — MEDIAN

Data: 3, 9, 5, 1, 7. A student wrote:

Step 1: Don't need to order — just find the middle position.
Step 2: Position 3 out of 5 values → 3rd value in original list = 5
Answer: Median = 5

Is the answer right? Is the method right? Explain.

The answer 5 happens to be correct, but the METHOD is wrong — this was a lucky accident. You must ALWAYS order the data first: 1, 3, 5, 7, 9 → median = 5. Without ordering, you'd get a wrong answer with a different data set.
ERROR ANALYSIS #3 — MODE

Data: 2, 5, 5, 8, 8, 9. A student wrote:

Step 1: 5 appears twice and 8 appears twice.
Step 2: Two values tie, so average them: (5 + 8) ÷ 2 = 6.5
Answer: Mode = 6.5

What is the student's error? What is the correct mode?

The student confused the MODE rule with the MEDIAN even-count rule. When two values tie for most frequent, BOTH are modes — you don't average them. The correct answer is: Mode = 5 AND 8 (bimodal).
ERROR ANALYSIS #4 — MEAN

Data: 10, 20, 30. A student wrote:

Step 1: The numbers go up by 10 each time.
Step 2: So the mean must be the middle one: Mean = 20

Is this answer correct? Is the reasoning valid for all data sets?

The answer (20) is accidentally correct here, but the reasoning is wrong and dangerous! The mean must always be calculated: (10+20+30)÷3 = 60÷3 = 20. The "middle value" approach only works for perfectly evenly spaced data — it fails for most real data sets.
ERROR ANALYSIS #5 — MEDIAN (EVEN COUNT)

Data: 6, 11, 14, 19. A student wrote:

Step 1: Ordered: 6, 11, 14, 19
Step 2: 4 values → even count → two middle values: 11 and 14
Step 3: Median = 14 (just pick the larger one)

What did the student do wrong? What is the correct median?

When there are two middle values, you must find their MEAN (average them), not just pick one. Correct median: (11+14)÷2 = 25÷2 = 12.5.

🧩 Missing Value

Work backwards! You're given the mean, median, or mode — find the missing number in the data set.

MISSING VALUE #1 — MEAN
The mean of these 5 numbers is 10. What is the missing value?
812915?
Work backwards
▶ Mean × Count = Total Sum needed: 10 × 5 =
▶ Known values sum: 8+12+9+15 =
▶ Missing value = Total − Known = − =
Missing value =
MISSING VALUE #2 — MEAN
The mean of 6 values is 15. Five of the values are: 12, 18, 10, 20, 14. Find the missing 6th value.
1218102014?
Missing value =

Mean×6 = 90. Known sum = 74. 90 − 74 = ?

MISSING VALUE #3 — MEDIAN
The median of these 5 ordered values is 13. Find the missing value.
710?1722
Think about position
▶ 5 values → the median is the rd value
▶ The 3rd position is currently ? → the median must equal 13, so ? =
Missing value =
MISSING VALUE #4 — MEDIAN (EVEN)
The median of these 4 ordered values is 9. Find the missing value.
48?15
Work backwards from the average
▶ Even count → median = average of 2nd and 3rd values
▶ (8 + ?) ÷ 2 = 9 → 8 + ? = → ? =
Missing value =
MISSING VALUE #5 — MODE
The mode of this data set is 7. Currently 7 appears only once. What could you add to the data set to make 7 the mode?
37954+?
MISSING VALUE #6 — CHALLENGE
A student has quiz scores of 78, 85, 92, 88. She wants a mean of at least 87 after 5 quizzes. What is the minimum score she needs on quiz 5?
78859288?
Min. score needed =

Target sum = 87 × 5 = 435. Current sum = 343. 435 − 343 = ?

🏆 Match It Up!

Match each description or example to Mean, Median, or Mode. Find all 6 pairs!

0
Matched
0
Flips
6
Total Pairs
🏆 Amazing! All 6 pairs matched! You know your measures of center! 🎉
MIXED REVIEW

All three — weather data

🌡️

9-Day Temperature Stretch

High temps (°F): 68, 72, 75, 72, 80, 72, 77, 68, 85

MEAN

Find the mean temperature. (Sum ÷ 9)

Sum = 669 → 669 ÷ 9 ≈ 74.3°F

MEDIAN

Order values and find the 5th (middle) value.

Ordered: 68, 68, 72, 72, 72, 72, 75, 77, 80, 85

MODE

Which temperature appears most often?

BEST MEASURE

The mean=74.3, median=72, mode=72. Which best represents "typical" temp here and why?

Median or Mode (both 72) are best — 72 appears 4 times and is the true center. The mean (74.3) is pulled up by the 85° outlier. When outliers exist, median is more representative than mean.