Since there are 6 values (even), find the average of the two middle values:
Middle 1 [ _______ ]
Middle 2 [ _______ ]
=
Sum [ _______ ]
÷ 2 =
Median _______
Which value occurs most often?
Mode = ______________
Maximum Value – Minimum Value
_______ – _______ = _______
Oz trading cards Curriculum • Large Print Page 2 of 3
How the Tin Man's 77 trading cards change the data.
Name: ______________________
Date: ______________________
🚨 OUTLIER INCIDENT: The Tin Man enters with a huge stack of 77 trading cards! When we include him, the Wicked Witch (8), and the Red slippers (1), our new sorted list of 9 values is:
1, 1, 6, 7, 7, 8, 15, 18, 77
Work out the statistical measures for the expanded set of 9 values.
New Mean (Average)
Sum: _______________________
Divide by 9: ______ ÷ 9 = ______
New Mean = _______
New Median (Middle)
List: 1, 1, 6, 7, 7, 8, 15, 18, 77
Find the exact middle value.
New Median = _______
New Mode
Which number(s) appear most often?
New Mode = _______
New Range
Max: _____ – Min: _____ =
New Range = _______
Explain your math reasoning in complete sentences in the spaces provided below.
1. What happened to the Mean when the Tin Man's outlier (77) was added? Why?
2. Did the Median change? Why is the Median so stable even with a huge outlier?
3. To describe the typical number of cards, is it better to use the Mean or Median?
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When explaining the Mean:
"Let's put all of their cards in one giant box. If we combine them, we have 54 cards total. Now, if we divide those 54 cards completely equally among our 6 travelers, what happens? Yes, each traveler gets exactly 9! That is the Mean. It is the 'fair share' value."
When introducing Slide 8 (Tin Man's 77 cards):
"Look at the Tin Man. He was extremely lucky and has 77 cards! When he joins the group, he has a HUGE number of cards compared to everyone else. He is what statisticians call an outlier. Let's make a prediction before we calculate: How will his giant number affect our Mean? Will it drag the average up? How will it affect our Median? Let's check!"
High-Level Analytical Question:
"If we tell people: 'On average, Oz travelers have about 18 trading cards' (the new Mean), is that true? Let's check: Toto has 1, Dorothy has 15, Wizard has 7... Almost EVERY traveler is BELOW 18 cards! Why is our Mean misleading us? Because the Tin Man's 77 is dragging it way up! That's why the Median (7) is a much better way to describe our typical traveler."
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Fully worked-out solutions and exemplary responses for grading.
Step 1 (Order Data): 1 < 6 < 7 < 7 < 15 < 18
Step 2 (Mean): Sum = 54. Division: 54 ÷ 6 = 9 cards.
Step 3 (Median): Middle values are 7 and 7. Average: (7 + 7) ÷ 2 = 7 cards.
Step 4 & 5 (Mode & Range): Mode = 7 (appears 2 times). Range: 18 – 1 = 17 cards.
Calculated Metrics (9 values: 1, 1, 6, 7, 7, 8, 15, 18, 77):
Q1. What happened to the Mean when Tin Man's outlier (77) was added?
"The mean jumped dramatically from 9 to 15.56. This happened because the mean combines all values together, so one extremely large number can raise the average of the whole group, even if the other values are small."
Q2. Did the Median change? Why is the Median so stable?
"No, the median stayed exactly 7. The median is stable because it only looks at which value is in the physical middle position of our sorted list. It does not care how large the maximum number is."
Q3. To describe a 'typical' traveler, would you use Mean or Median?
"I would use the Median (7). Almost all characters have less than 15 cards. The mean of 15.56 is higher than 7 of our 9 travelers, which makes it misleading. The median of 7 shows the true middle of the group."
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