Stat Squad Slides Stat Squad Training
Mastering Mean, Median, Mode, and Range
The Mission
"As a member of the Stat Squad, your job is to describe a group of numbers using four special tools."
1 Find the Average (Mean)
2 Find the Middle (Median)
3 Find the Most Frequent (Mode)
4 Find the Gap (Range)
Mode: The Popular One
Definition:
The number that appears most often in the set.
Clue:
"Mode" starts with MO, just like MOst often!
Example Set:
2
5
2
8
3
Mode = 2
Median: The Middle
The middle value when numbers are in order from least to greatest.
Step-by-Step:
1
Line them up: 2, 3, 5, 8, 9
2
Cross off one from each side until you hit the center.
2
3
5
8
9
Mean: The Average
The "fair share" value. If everyone had the same amount, what would it be?
Formula:
Sum of all numbers
Count of numbers
Numbers: 2, 4, 6
1. Add: 2 + 4 + 6 = 12
2. Count: There are 3 numbers.
3. Divide: 12 ÷ 3 = 4
Range: The Spread
The distance between the Highest number and the Lowest number.
9
Highest
2
Lowest
7
Range
Data Detectives Worksheet Stat Squad Training
Level 1: Single-Digit Data Mission
Name:
Date:
MODE
Most Often
MEDIAN
Middle
MEAN
Average
RANGE
Spread
CASE #1
The Lucky Dice
1
3
4
4
8
Step 1: Find the MODE
The number that appears most often.
Step 2: Find the RANGE
Highest minus Lowest.
Step 3: Find the MEDIAN
Line them up in order and find the exact middle.
1
3
4
4
8
Middle Number:
Step 4: Find the MEAN
A) Add them up:
1 + 3 + 4 + 4 + 8 =
B) Divide by count (5):
÷ 5 =
CASE #2
The Scoring Streak
The basketball team scored these points in 5 games: 3, 7, 3, 9, 8
1. Put numbers in order (Least to Greatest):
Mode
Detective Scratchpad
Range
-
=
Median
Detective Scratchpad
Mean
Add: ___ + ___ + ___ + ___ + ___ = ___
Divide: ___ ÷ 5 = ___
CASE #3
The Field Detective
Find the stats for this data set: 4, 4, 1, 6, 9
Mode
Median
Mean
Range
Data Detectives Answer Key Answer Key
Stat Squad Training: Level 1
Teacher Resource
Case #1
The Lucky Dice (1, 3, 4, 4, 8)
Mode
4
Median
4
Mean
4
20 ÷ 5
Range
7
8 - 1
Case #2
The Scoring Streak (3, 7, 3, 9, 8)
Ordered: 3, 3, 7, 8, 9
Mode
3
Median
7
Mean
6
30 ÷ 5
Range
6
9 - 3
Case #3
The Field Detective (4, 4, 1, 6, 9)
Mode
4
Median
4
1, 4, 4, 6, 9
Mean
4.8
24 ÷ 5
Range
8
9 - 1
Teaching Tips
• Level 1 Goal: Focus on the process . Encourage students to check their ordering twice before finding the Median.
• Case 1: Balanced set (Sum=20, Count=5) creates a clear Mean of 4.
• Case 3 Challenge: Introduces 4.8. Remind students that averages aren't always whole numbers.
• Range Visual: Emphasize "Subtracting the smallest from the largest" to avoid negative number confusion.
Stat Squad Exit Ticket Final Case
Stat Squad Exit Ticket
Level 1 Final Assessment
Name:
The Evidence: 2, 9, 5, 2, 7
Step 1: Put numbers in order
Mode (Most Often)
Median (Middle)
Mean (Add & Divide)
Sum: ____ ÷ 5 =
Range (High - Low)
Show Calculations Below
Final Case
Stat Squad Exit Ticket
Level 1 Final Assessment
Name:
The Evidence: 2, 9, 5, 2, 7
Step 1: Put numbers in order
Mode (Most Often)
Median (Middle)
Mean (Add & Divide)
Sum: ____ ÷ 5 =
Range (High - Low)
Show Calculations Below
Exit Ticket Answer Key Answer Key
Exit Ticket: Final Data Clearance
Teacher Guide
Mission Data
2, 9, 5, 2, 7
Mode
2
The number 2 appears twice.
Median
5
Ordered: 2, 2, 5, 7, 9
Mean
5
Sum (25) ÷ Count (5) = 5
Range
7
High (9) - Low (2) = 7
Evaluation Notes
• Median Error: Watch for students who don't re-order the set (median would incorrectly be 5, but by accident if they just picked the middle of 2, 9, 5, 2, 7). Check their scratch work for the ordered list: 2, 2, 5, 7, 9.
• Mean Calculation: The sum of 25 was chosen to make the division by 5 very clean for students.
Stat Squad Pro Slides Double Digit Mission
Stat Squad: Level 2
The Level Up
The logic is the same.
New Challenge
Double-digit addition
Long division for Mean
Multi-step range checks
Mission Data
12 45 28 12
Pro Tip: Median
Double-Check Your Order!
With bigger numbers, it's easy to skip one. Cross them off the original list as you write your new ordered list.
Original:
45, 12, 28, 12
Ordered:
12, 12, 28, 45
Pro Tip: Mean
Use the Stack!
Add double-digit numbers by lining up the ones and tens place carefully.
"The sum will be much larger now. Don't rush the addition!"
12
45
28
+ 12
97
Mode & Range
Mode
Look for twins! Multiple pairs? List them all. No twins?
12, 12, 28, 45 → 12
Range
Subtract the smallest from the largest .
45 - 12 = 33
Double Digit Data Worksheet Stat Squad Pro
Level 2: Double-Digit Data Mission
Name:
Date:
MISSION #1
The Tech Lab Scores
Data Set: 15, 22, 18, 15, 30
1. Order Data (L → G)
Mode
Median
Range: High - Low
-
=
Mean Machine
15
22
18
15
+ 30
Sum
Sum ÷ 5
Mean
MISSION #2
The Field Samples
Heights (cm): 42, 38, 42, 50, 42, 50
Scratchpad: Order & Calculate
Mode
Median
Mean
Range
Independent Case Files
Stat Squad Pro • Page 2
MISSION #3
Unsorted Intel
Data Set:
25, 12, 18, 25, 20
Mode
Median
Mean (Sum ÷ 5)
Range (H-L)
MISSION #4
The Delivery Log
Data Set:
14, 18, 20, 14, 24
Mode
Median
Mean (Sum ÷ 5)
Range (H-L)
MISSION #5
The Temperature Watch
Data Set:
22, 28, 22, 26, 30, 34
Mode
Median
Mean (Sum ÷ 6)
Range (H-L)
I ordered my lists, checked my sums, and verified my subtraction.
Double Digit Answer Key Answer Key
Level 2: Double-Digit Mission
Pro Resource
Mission #1
The Tech Lab Scores (15, 22, 18, 15, 30)
Mode
15
Median
18
15, 15, 18, 22, 30
Mean
20
Sum: 100 ÷ 5
Range
15
30 - 15
Mission #2
The Field Samples (42, 38, 42, 50, 42, 50)
Mode
42
Median
42
38, 42, 42, 42, 50, 50
Mean
44
Sum: 264 ÷ 6
Range
12
50 - 38
Mission #3
Unsorted Intel (25, 12, 18, 25, 20)
Mode
25
Median
20
12, 18, 20, 25, 25
Mean
20
Sum: 100 ÷ 5
Range
13
25 - 12
Mission #4
The Delivery Log (14, 18, 20, 14, 24)
Mode
14
Median
18
14, 14, 18, 20, 24
Mean
18
Sum: 90 ÷ 5
Range
10
24 - 14
Mission #5
The Temperature Watch (22, 28, 22, 26, 30, 34)
Mode
22
Median
27
22, 22, 26, 28, 30, 34
Mean
27
Sum: 162 ÷ 6
Range
12
34 - 22
Pro Level Evaluation Tips
• Addition: Multi-digit addition is the primary hurdle. Verify Addition Stacks first.
• Median Even Sets: Missions #2 and #5 have 6 items. Median is the average of the two middle numbers.
• Whole Numbers: Most sets are designed to yield whole number means to keep focus on concepts.
Level 2 Exit Ticket Pro Level
Pro Exit Ticket
Mission: Double Digit Clearance
Name:
Target Data Stream
14 25 14 20 27
Mode
Median (Order First!)
Mean (Average)
Sum (____) ÷ 5 =
Range (H - L)
Scratchpad (Show Addition/Ordering)
Cut Here
Pro Level
Pro Exit Ticket
Mission: Double Digit Clearance
Name:
Target Data Stream
14 25 14 20 27
Mode
Median (Order First!)
Mean (Average)
Sum (____) ÷ 5 =
Range (H - L)
Scratchpad (Show Addition/Ordering)
Level 2 Exit Ticket Key Answer Key
Level 2 Exit Ticket: Pro Level
Final Validation
Target Intel
14, 25, 14, 20, 27
Mode
14
(Appears Twice)
Median
20
Ordered: 14, 14, 20, 25, 27
Mean
20
Sum (100) ÷ Count (5) = 20
Range
13
High (27) - Low (14) = 13
Level 2 Mastery Check
Students who correctly identify the Median as 20 likely ordered the numbers correctly. If they chose 14 (the middle of the unsorted list), they skipped the ordering step.
The sum is exactly 100 to reward students who performed the addition correctly without making the division overly punishing at the end of the lesson.
Case Files Practice Pack Top Secret
Case Files Practice Pack
Data Detective Academy: Independent Practice
Agent:
Date:
"Agents, we have several cold cases that need statistical analysis. Use your tools—Mean, Median, Mode, and Range. Remember to order your data first!"
1
Case #101: The Dice Roll
Level 1
Data: 4, 7, 2, 4, 8
Order the data stream & Scratchpad:
Mean:
Median:
Mode:
Range:
2
Case #102: Game Scores
Level 1
Data: 12, 15, 12, 10, 21
Order the data stream & Scratchpad:
Mean:
Median:
Mode:
Range:
3
Case #103: Pet Weights
Level 1
Data: 5, 8, 5, 12, 8, 4
Order the data stream & Scratchpad:
Mean:
Median:
Mode:
Range:
4
Case #104: Lunch Costs
Level 1
Data: 7, 9, 6, 8, 10
Order the data stream & Scratchpad:
Mean:
Median:
Mode:
Range:
Cold Case Files Continued
Page 2
5
Case #105: Thermal Check
Daily high temperatures (°F): 72, 68, 72, 80, 75, 71, 75
Level 2
Order the data stream
Scratchpad / Calculations
Mean
Median
Mode
Range
6
Case #106: The Distance Run
Meters run by the squad: 45, 52, 45, 50, 48
Level 2
Order the data stream
Scratchpad / Calculations
Mean
Median
Mode
Range
Mission Summary
Files Cleared: ____ / 6
Self
Pro
Case Files Answer Key Answer Key
Case Files Practice Pack: Official Record
Pro Resource
1
#101: 4, 7, 2, 4, 8
Mean:5
Median:4
Mode:4
Range:6
2, 4, 4, 7, 8 | Sum: 25
2
#102: 12, 15, 12, 10, 21
Mean:14
Median:12
Mode:12
Range:11
10, 12, 12, 15, 21 | Sum: 70
3
#103: 5, 8, 5, 12, 8, 4
Mean:7
Median:6.5
Mode:5, 8
Range:8
4, 5, 5, 8, 8, 12 | Sum: 42
4
#104: 7, 9, 6, 8, 10
Mean:8
Median:8
Mode:None
Range:4
6, 7, 8, 9, 10 | Sum: 40
5
#105: 72, 68, 72, 80, 75, 71, 75
Mean
73.3
513 ÷ 7
Median
72
68, 71, 72, 72, 75, 75, 80
Mode
72, 75
Bimodal
Range
12
80 - 68
6
#106: 45, 52, 45, 50, 48
Mean
48
240 ÷ 5
Median
48
45, 45, 48, 50, 52
Mode
45
Range
7
52 - 45
Grading Insights
• #103 Median: Ordered list {4, 5, 5, 8, 8, 12}. Middle two numbers are 5 and 8. The median is the average: (5 + 8) ÷ 2 = 6.5.
• #104 Mode: Ensure students write "None". Writing "0" is technically incorrect as 0 is not in the set.
• #105 Bimodal: Both 72 and 75 appear twice. Both must be listed for full clearance.
Mystery extraction Slides The Narrative Intel
Solving Word Problem Mysteries
Hidden Evidence
In real life, data isn't always listed neatly. It's hidden inside stories and reports.
"The suspect stole 4 diamonds on Monday, 7 on Tuesday, and 4 on Wednesday..."
Extract the Data Set: {4, 7, 4}
1. Scan for Numbers
2. List the Intel
3. Order & Analyze
Extraction Training
"I saw the thief escape in a car. Over the last four days, I've seen him pass by 3 times on Monday, 8 times on Tuesday, 3 times on Wednesday, and 6 times today."
Raw Intel
3, 8, 3, 6
Ordered Intel
3, 3, 6, 8
Solving for Mean
In word problems, the mean is often called the Average.
Pro Tip:
Always double check the COUNT. If the story lists 5 days, you must divide by 5.
Numbers: 3, 3, 6, 8
Sum: 20
Count: 4
Mean: 5
The Median Trap
Don't pick the middle of the story!
Word problems often put the numbers out of order on purpose. You MUST list them from least to greatest before finding the median.
Wrong Way
Story: 8, 2, 5 → Median: 2
The Squad Way
Sorted: 2, 5, 8 → Median: 5
Practice Mission A
Extract the Intel
"A detective found 12 clues on the first floor, 5 on the second, 8 in the basement, and 15 in the attic."
Ordered Set
5, 8, 12, 15
Mean
10
Median
10
Practice Mission B
Master the Mode
"Suspect #4 wore a blue shirt 3 times this month, a red shirt 7 times, a blue shirt again 2 more times, and a white shirt 3 times."
The Secret Set
3, 7, 2, 3
The Mode
3
Mystery Logs Worksheet The Mystery Logs
Level 3: Narrative Data Extraction
Agent:
Date:
"Agents, data is hidden in these stories. Extract the evidence, organize it, and solve for the required stats. Don't let the narrative order deceive you!"
1
The Library Heist
"A thief took books from the library. The log shows: 12 books on Monday, 8 on Tuesday, 15 on Wednesday, 12 on Thursday, and 13 on Friday."
Order Evidence Stream
Mean
Median
Mode
2
The Training Camp
"Recruits practiced sprinting. Over six trials, Agent J ran 40 meters, 55 meters, 40 meters, 60 meters, 40 meters, and 65 meters."
Order Evidence Stream
Mode
Range
Median
3
The Jewels of Nile
"Curator Z needs stats on diamond weights (carats): 15, 20, 10, 20, and 25."
Order
Mean
Median
Mode
Range
!
The False Report Case
"A suspect claimed an average of $10 per day on lunch. Their statement shows: $12, $15, $5, $22, and $6."
Prove your case (Show Mean Calculation):
Actual Mean: $___________
Official Verdict
Was the suspect lying? Why?
Mystery Logs Answer Key Answer Key
Lesson 4: Narrative Solutions & Logic
Official Clearance
1
The Library Heist (12, 8, 15, 12, 13)
Ordered Data
8, 12, 12, 13, 15
Mean
12
60 ÷ 5
Median
12
Mode
12
2
The Training Camp (40, 55, 40, 60, 40, 65)
Ordered Data
40, 40, 40, 55, 60, 65
Mode
40
Range
25
65 - 40
Median
47.5
(40+55)/2
3
Jewels (15, 20, 10, 20, 25)
Ordered Data
10, 15, 20, 20, 25
Mean
18
Median
20
Mode
20
Range
15
!
Verdict: False Report
Calculation:
$12 + $15 + $5 + $22 + $6 = $60 total.
Verdict Analysis:
Suspect was LYING. The actual average was $12, not $10.
Teaching Notes
• Median Trap: Check Problem 1. Middle number in narrative is 15, but actual median is 12. Picking 15 means they didn't sort.
• Case 2 Median: Even set (6). Middle values are 40 and 55. Average is 47.5. Accept 47 or 48 if rounding logic is consistent.
• Application: Problem 4 uses statistics for validation/logic rather than just calculation.
Academy Final Evaluation Test Academy Final
Stat Squad Certification
Data Detective Academy: Level 1-3 Comprehensive Evaluation
Agent:
Date:
Part 1: Detective Definitions
Match the statistical tool to its correct definition by writing the letter in the box.
1. Mean
2. Median
3. Mode
4. Range
A. The difference between the largest and smallest numbers in a set.
B. The number(s) that appear most frequently in a data stream.
C. The "Fair Share" or Average. Found by adding and then dividing.
D. The exact middle value when a set is ordered least to greatest.
Part 2: Rookie Training (Level 1)
Analyze the following Evidence Stream: 9, 2, 4, 3, 2
Mean
Median
Mode
Range
Show ordering or addition work below
Part 3: Pro Clearance (Level 2)
Double-Digit Intelligence Stream:
24 18 22 18 38
Addition Stack (Sum)
24
18
22
18
+ 38
Order the data stream
Mean
Median
Mode
Range
Part 4: Narrative Investigation
"Recruit Agent K is investigating a series of safe house entries. Over the last seven days, sensors detected 5 entries on Monday, 2 on Tuesday, 5 on Wednesday, 8 on Thursday, 5 on Friday, 10 on Saturday, and 7 on Sunday."
Extracted Order (L → G)
Average (Mean) Entries
Middle (Median) Value
Part 5: Master Challenge
The Chief says his department solves an average of 15 cases per month. Using the intelligence stream below, prove if the Chief is accurate.
12, 10, 25, 8, 15
Prove your case (Calculation)
Final Verdict (Accurate? Why?)
Academy Final Evaluation Answer Key Answer Key
Academy Final: Stat Squad Certification
Official Record
Part 1: Definitions
1. Mean
C
2. Median
D
3. Mode
B
4. Range
A
Part 2: Rookie Training (9, 2, 4, 3, 2)
Ordered Stream: 2, 2, 3, 4, 9 | Sum: 20
Mean
4
20 ÷ 5
Median
3
Mode
2
Range
7
9 - 2
Part 3: Pro Clearance (24, 18, 22, 18, 38)
Ordered Stream: 18, 18, 22, 24, 38 | Sum: 120
Mean
24
120 ÷ 5
Median
22
Mode
18
Range
20
38 - 18
Part 4: Narrative Investigation
Ordered: 2, 5, 5, 5, 7, 8, 10 | Sum: 42
Mean (Average)
6
42 ÷ 7 days
Median (Middle)
5
Exact center of 7 items
Part 5: Master Challenge Verdict
Calculation Path:
Sum: 12 + 10 + 25 + 8 + 15 = 70
Mean: 70 ÷ 5 = 14
Final Clearance:
The Chief is INACCURATE.
Grading Strategy
Critical Check - Part 4: Watch for the 'Narrative Trap'. Many recruits will pick 8 as the median because it is the middle value mentioned in the story. Verify they have ordered the list (2, 5, 5, 5, 7, 8, 10) to earn their certification.
High School Statistics Test Assessment Statistical Foundations Assessment
Data Analysis Proficiency: Advanced Level
Student:
Date:
1 Primary Dataset Analysis
{ 14.5, 22.8, 19.2, 14.5, 30.1, 18.7, 25.2, 11.0 }
A. Mean (Average):
B. Median:
C. Mode(s):
D. Range:
Scratchpad Area:
2 Algebraic Applications
A student has exam scores of 82, 88, 91, and 79 . What score must they earn on the fifth exam to achieve a target mean score of exactly 87 ?
Algebraic Work
Required Score
3 Frequency Distribution Analysis
Hours (x) Frequency (f) 5 4 10 6 15 8 20 2 Sum Frequency
Mean Calculation Work:
Calculated Mean:
4 Theoretical Outlier Analysis
Salary Data: { $45k, $48k, $52k, $45k, $50k, $210k }
1. Which measure of central tendency would be significantly inflated by the outlier ($210k)?
Mean
Median
Mode
2. Justify your answer. Explain how extreme outliers affect data distribution.
5 Strategic Data Comparison
Group A Scores: 72, 75, 74, 73, 76
Calculate the Range for both. Explain which group is more consistent using numerical evidence.
Mathematical Calculations
Final Conclusion
High School Statistics Answer Key Answer Key
High School Statistics Assessment: Teacher Reference
Standardized Key
1. Primary Dataset Analysis
Ordered Set: { 11.0, 14.5, 14.5, 18.7, 19.2, 22.8, 25.2, 30.1 }
A. Mean (x̄): 19.50
B. Median: 18.95
C. Mode: 14.5
D. Range: 19.1
Calculations:
• Sum (Σx) = 156.0
• Mean = 156.0 / 8 = 19.5
• Median = (18.7 + 19.2) / 2 = 18.95
• Range = 30.1 - 11.0 = 19.1
2. Algebraic Resolution
Step-by-Step Path:
(82 + 88 + 91 + 79 + x) / 5 = 87
Correct Score
95
3. Grouped Data Distribution
x f x * f 5 4 20 10 6 60 15 8 120 20 2 40 Sum 20 240
Mean = Σ(xf) / Σf
240 / 20 =
12
4. Theoretical Justification
Inflated Measure: Mean
The mean is highly sensitive to extreme values because every entry in the data set contributes directly to the total sum. A high outlier pulls the sum upward significantly. In contrast, the median identifies the positional midpoint (50th percentile) and is resistant to the specific magnitude of outliers.
5. Comparative Verdict
Data Ranges:
• Group A: 76 - 72 = 4
• Group B: 100 - 55 = 45
Conclusion:
Group A is demonstrably more consistent. Their range of 4 (compared to Group B's 45) proves that their scores are tightly clustered around the center without wide variance.
