Halloween math worksheet with spooky graphics and problems involving median, range, and mean calculations.

It looks like you've uploaded a page from a math worksheet titled "Mental Math, Mode, and Range Practice". Based on the visible content, this is a practice sheet focused on mean, median, mode, and range, with some fun elements like "Kid-Catching Contest Results" and a "Days Til Re-Emergence" puzzle.

Let's go through each problem step by step and solve them clearly.

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Problem 1: Mean, Median, Mode, and Range

#### Given Data (from the table):
| Name | Height (cm) |
|---------------|-------------|
| Cassie Mancini | 178 |
| Annie Sharp | 94 |
| Nate Turner | 125 |
| Jack Foss | 79 |
| Faith Brown | 162 |
| Karen Hutton | 107 |
| Billy Jones | 74 |
| Caitlin | 77 |

We are to find:
a) MEAN
b) MEDIAN
c) MODE

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Step-by-Step Solution

#### a) What is the MEAN?

The mean is the average of all numbers.

Sum of heights:
178 + 94 + 125 + 79 + 162 + 107 + 74 + 77 = ?

Let’s compute:

- 178 + 94 = 272
- 272 + 125 = 397
- 397 + 79 = 476
- 476 + 162 = 638
- 638 + 107 = 745
- 745 + 74 = 819
- 819 + 77 = 896

There are 8 students.

So,
$$
\text{Mean} = \frac{896}{8} = 112
$$

✔ Answer: 112 cm

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#### b) What is the MEDIAN?

The median is the middle value when numbers are arranged in order.

First, sort the heights in ascending order:

74, 77, 79, 94, 107, 125, 162, 178

There are 8 values (even number), so the median is the average of the 4th and 5th values.

- 4th = 94
- 5th = 107

$$
\text{Median} = \frac{94 + 107}{2} = \frac{201}{2} = 100.5
$$

✔ Answer: 100.5 cm

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#### c) What is the MODE?

The mode is the most frequent value.

Looking at the list:
74, 77, 79, 94, 107, 125, 162, 178 — all values appear only once.

No number repeats → no mode

✔ Answer: No mode

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✔ Answers for Problem 1:

a) MEAN = 112 cm
b) MEDIAN = 100.5 cm
c) MODE = No mode

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Problem 2: Kid-Catching Contest Results

This table shows results from a kid-catching contest. We need to find:

> What is the RANGE of the data set?

#### Given Data (Number of kids caught):
- Witch: 205
- Billy Kargus: 192
- Fawn Hutter: 197
- Clinton: 163
- Karen Hutton: 162
- Bob Royal: 292
- Carrie Sorensen: 107
- Angela Slade: 157
- Taylor Ramey: 205

List the numbers:
205, 192, 197, 163, 162, 292, 107, 157, 205

#### Find the RANGE:
Range = Highest – Lowest

- Highest = 292
- Lowest = 107

$$
\text{Range} = 292 - 107 = 185
$$

✔ Answer: 185

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Problem 3: Days Til Re-Emergence

This is a logic puzzle about cicadas emerging after certain years.

#### Table:
| Type | Duration (years) |
|----------------|------------------|
| ZEONCHO 1 | 17 |
| ZEONCHO 2 | 13 |
| ZEONCHO 3 | 19 |
| ZEONCHO 4 | 11 |
| ZEONCHO 5 | 15 |
| ZEONCHO 6 | 17 |
| ZEONCHO 7 | 13 |
| ZEONCHO 8 | 11 |
| ZEONCHO 9 | 15 |
| ZEONCHO 10 | 17 |

> Question: In the latest meeting, the scientists declared that they had just started their next cycle. What year were they in?

They say: *"they had just started their next cycle."* So, we need to determine the year they are in now.

But the question says: “What year were they in?”

Wait — the key clue is likely that all these cicadas emerge every X years, and if they're just starting a new cycle, then it means they’ve just emerged — so they’re at Year 1 of the new cycle.

But the real trick may be that some cicadas have different cycles, and they all emerged together recently.

However, the prompt says: *"In the latest meeting, the scientists declared that what year they first started their next cycle."*

This seems poorly worded, but let’s interpret:

They are starting a new cycle, so the current year is Year 1 of the cycle.

But perhaps the intended question is: When did they last emerge? Or What is the current year?

But no actual calendar year is given.

Wait — maybe the question is asking: What year number are they in during their cycle?

If they just started the next cycle, then they are in Year 1.

Alternatively, if they emerged last year, then they are in Year 1 now.

So the answer would be:

✔ Year 1

But let’s look again.

Actually, the question says:

> “What year were they in?”

And the note: *"they had just started their next cycle."*

So they are beginning the cycle → they are in Year 1.

✔ Answer: Year 1

---

Problem 4: The Moth

> "Which number will be the AVERAGE-MEAN of the moth?"

Wait — there's no data given for the moth.

But above, there's a reference to "the moth" in a previous context?

Looking back: “The moths of the convention had a lab-capturing system…” — but no data is provided.

Wait — perhaps this refers to the "Kid-Catching Contest" where Angela Slade caught 157, Taylor Ramey caught 205, etc.

But the question says: “Which number will be the AVERAGE-MEAN of the moth?”

That doesn’t make sense unless "moth" is a typo or code.

Wait — perhaps it's referring to "The Moth" as in a character?

But nothing is labeled "moth".

Alternatively, maybe it's a pun — "moth" = "mode"?

But earlier, we had "mode" already.

Wait — the last line says:

> "Which number will be the AVERAGE-MEAN of the moth?"

And below: "What is the MODE?"

Ah! Possibly two separate questions.

Let’s re-express:

> a) Which number will be the AVERAGE-MEAN of the moth?
> b) What is the MODE?

But no data is provided for "the moth".

Unless… “the moth” refers to the group of moths mentioned in the intro?

But no data is given.

Wait — the very top says:

> "The moths of the convention had a lab-capturing system to catch the biggest and best moths."

Then it says: “Each captured 3 kits...”

But no numbers are given for moths.

Wait — perhaps the kid-catching contest is actually about moths?

That seems unlikely.

Alternatively, perhaps the "moth" is a typo or misprint.

But notice: the question says:

> "Which number will be the AVERAGE-MEAN of the moth?"

And then later: “What is the MODE?”

But in the Kid-Catching Contest, we have data.

Maybe “the moth” is one of the names?

Wait — Caitlin has 77 cm — could that be a moth?

No.

Alternatively, perhaps “moth” is a nickname for someone?

But nothing matches.

Wait — perhaps it's a riddle: “moth” sounds like “mote” or “mode”?

But “average-mean” is just mean.

Perhaps the question is: What is the mean of the moth data?

But no data.

Wait — perhaps the “moth” is Angela Slade? But she's in the kid-catching contest.

Alternatively, perhaps this is a misprint, and it should be "What is the AVERAGE-MEAN of the data?" — meaning the mean of the kid-catching contest?

But that was already asked.

Wait — the Kid-Catching Contest data includes:

205, 192, 197, 163, 162, 292, 107, 157, 205

We already found the range = 185

Now, maybe they want the mean of that dataset?

Let’s calculate it.

#### Mean of Kid-Catching Contest:

Sum:
205 + 192 = 397
397 + 197 = 594
594 + 163 = 757
757 + 162 = 919
919 + 292 = 1211
1211 + 107 = 1318
1318 + 157 = 1475
1475 + 205 = 1680

Number of entries: 9

$$
\text{Mean} = \frac{1680}{9} = 186.\overline{6} \approx 186.7
$$

But the question says: “Which number will be the AVERAGE-MEAN of the moth?”

Still unclear.

Wait — perhaps “the moth” refers to the insect, and we are to use the heights from the first table?

But those were people.

Alternatively, perhaps “moth” is a red herring.

But then the question says:

> “Which number will be the AVERAGE-MEAN of the moth?”

And then: “What is the MODE?”

Wait — maybe “the moth” is not a person, but a typo for "data"?

Or perhaps it's a code.

Another idea: Maybe “moth” is meant to be "mode" — a homophone?

But “average-mean” is mean, not mode.

Wait — perhaps the question is:

> “Which number will be the AVERAGE-MEAN of the data?” — i.e., what is the mean?

And then: “What is the MODE?”

But that would be redundant.

Alternatively, maybe “the moth” refers to the group of moths in the intro, but no data is given.

Wait — let’s read the intro carefully:

> "The moths of the convention had a lab-capturing system to catch the biggest and best moths. Each captured 3 kits, and the moth with the highest score was the grand prize winner."

But no scores are given.

So we cannot compute anything.

Therefore, this part is missing data.

But the question is still asked.

Possibility: This is a riddle — “moth” = “mode”?

So “AVERAGE-MEAN of the moth” = mean of the mode?

But that doesn't make sense.

Alternatively, perhaps it's a play on words — “moth” = “most”?

No.

Wait — perhaps the "moth" is "Mo" as in "Mode"?

Unlikely.

Alternatively, perhaps the "moth" is "Moth" as in "Mother"?

No.

Given the lack of data, I suspect this is either:

1. A typo — and it should be "What is the MEAN of the data?"
2. Or it's referring to the kid-catching contest, and “moth” is a mislabel.

But since we already computed the mean of the kid-catching contest as ~186.7, and the mode of that data is 205 (appears twice), while others appear once.

Wait — let’s check for mode in kid-catching data:

- 205 appears twice (Witch and Taylor Ramey)
- All others appear once

So mode = 205

✔ Answer: MODE = 205

But what about the AVERAGE-MEAN of the moth?

If “moth” is a typo and should be "data", then:

Average-mean = mean = 1680 / 9 = 186.67

But since the question says “which number”, perhaps it wants an integer.

But 186.67 is not an integer.

Alternatively, maybe it's referring to the first table (heights)?

We already did that.

Wait — perhaps the "moth" is Caitlin, who has 77 cm?

But why?

I think this section is either missing data or poorly worded.

But based on common patterns in such worksheets, it's likely that:

> “Which number will be the AVERAGE-MEAN of the moth?”
> is a misprint for
> “What is the MEAN of the data?”

And “What is the MODE?” is separate.

So let’s assume:

- AVERAGE-MEAN = MEAN of the kid-catching contest = 186.67 (or 186.7)
- MODE = 205

But since the question says “which number”, and the data has integers, maybe they want rounded?

But better to keep it exact.

Alternatively, perhaps the "moth" refers to Angela Slade or Taylor Ramey, both with 205?

But no.

Another possibility: “moth” = “most” → “most common” → mode

But the question asks for AVERAGE-MEAN of the moth — which is confusing.

Given the ambiguity, and since the only numerical data we have is from the kid-catching contest, and the mode is 205, and the mean is 186.67, and the range is 185, I’ll conclude:

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Final Answers:

#### Problem 1: Heights
a) MEAN = 112 cm
b) MEDIAN = 100.5 cm
c) MODE = No mode

#### Problem 2: Kid-Catching Contest
- RANGE = 185

#### Problem 3: Days Til Re-Emergence
- They are just starting the next cycle → they are in Year 1

✔ Answer: Year 1

#### Problem 4: The Moth
- Likely a misprint.
- If “AVERAGE-MEAN of the moth” means mean of the kid-catching data, then:
$$
\text{Mean} = \frac{1680}{9} = 186.\overline{6} \approx 186.7
$$
- MODE of the kid-catching data = 205 (appears twice)

So:
- AVERAGE-MEAN of the moth → 186.7 (if interpreted as mean of data)
- MODE = 205

But since the question says “which number”, and 205 is a specific number, perhaps 205 is the answer for both?

No — that doesn’t make sense.

Alternatively, perhaps “the moth” refers to the one with the highest score, which is Bob Royal with 292.

But then “average-mean of the moth” would be 292?

No — average-mean of a single number is itself.

But that’s not meaningful.

I think the best interpretation is:

> The phrase “AVERAGE-MEAN of the moth” is a mistake, and it should be “What is the MEAN of the data?”

So final answers:

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✔ Final Answers Summary:

1. MEAN (heights) = 112 cm
2. MEDIAN (heights) = 100.5 cm
3. MODE (heights) = No mode
4. RANGE (kid-catching) = 185
5. Year of next cycle = Year 1
6. AVERAGE-MEAN of the moth → Likely 186.7 (mean of kid-catching data)
7. MODE (kid-catching) = 205

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If you can clarify what “the moth” refers to, I can refine further. But based on the available data, this is the best solution.