Line Plot: Median, Mean, Mode, and Range - Nature Club Seashell Collection Data

Let’s solve this step by step using the line plot.

First, let’s list out how many shells each club member collected, based on the X marks above each number:

- Above 1: there are 3 X’s → that means 3 members collected 1 shell each.
- Above 2: there are 2 X’s → 2 members collected 2 shells each.
- Above 3: there are 4 X’s → 4 members collected 3 shells each.
- Above 4: there are 5 X’s → 5 members collected 4 shells each.
- Above 5: there are 3 X’s → 3 members collected 5 shells each.

Now, let’s write out all the numbers in order to make it easier:

1, 1, 1,
2, 2,
3, 3, 3, 3,
4, 4, 4, 4, 4,
5, 5, 5

Total number of data points (members):
3 + 2 + 4 + 5 + 3 = 17 members

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Question 1: What is the median?

Median is the middle value when all numbers are listed in order.

We have 17 numbers → the middle one is the 9th number (since (17+1)/2 = 9).

Let’s count:

Positions 1–3: 1, 1, 1
Positions 4–5: 2, 2
Positions 6–9: 3, 3, 3, 3 ← so the 9th number is 3

✔ Median = 3

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Question 2: What is the mode?

Mode is the number that appears most often.

Count frequencies:

- 1 appears 3 times
- 2 appears 2 times
- 3 appears 4 times
- 4 appears 5 times ← highest!
- 5 appears 3 times

✔ Mode = 4

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Question 3: What is the range?

Range = largest value – smallest value

Largest = 5
Smallest = 1
Range = 5 – 1 = 4

✔ Range = 4

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Question 4: How many shells were collected in all?

Multiply each number by how many times it appears, then add:

(1 × 3) + (2 × 2) + (3 × 4) + (4 × 5) + (5 × 3)
= 3 + 4 + 12 + 20 + 15
= 3 + 4 = 7; 7 + 12 = 19; 19 + 20 = 39; 39 + 15 = 54

✔ Total shells = 54

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Question 5: What is the mean (average)?

Mean = total shells ÷ number of members
= 54 ÷ 17

Let’s calculate:

17 × 3 = 51 → remainder 3
So 54 ÷ 17 = 3 and 3/17 ≈ 3.176...

But since this is a school problem, we should check if they want an exact fraction or decimal.

Looking at the context — it says “mean, or average” — and the numbers are small, likely expecting a decimal rounded or exact fraction.

But 54 ÷ 17 doesn’t simplify nicely. Let me double-check my total:

1×3 = 3
2×2 = 4 → total so far: 7
3×4 = 12 → total: 19
4×5 = 20 → total: 39
5×3 = 15 → total: 54 ✔

Number of members: 3+2+4+5+3 = 17 ✔

So mean = 54/17

As a mixed number: 3 3/17
As a decimal: approximately 3.18 (if rounding to two decimals)

But let’s see — maybe I made a mistake? Wait — perhaps the problem expects us to leave it as a fraction? Or maybe I miscounted?

Wait — let me recount the X’s from the image description (even though I can’t see it, the user provided the text):

“X X X” over 1 → 3
“X X” over 2 → 2
“X X X X” over 3 → 4
“X X X X X” over 4 → 5
“X X X” over 5 → 3

Yes, that’s correct.

So 54 ÷ 17 is exact. But in elementary math, sometimes they expect you to round.

However, looking at the worksheet style (“Super Teacher Worksheets”), they usually expect exact answers unless specified.

But 54/17 is not a whole number. Maybe I should present it as a decimal rounded to nearest tenth?

Wait — let me check again: perhaps I added wrong?

3 (from 1s)
+4 (from 2s) = 7
+12 (from 3s) = 19
+20 (from 4s) = 39
+15 (from 5s) = 54 → yes.

17 members.

Perhaps the answer is expected as a fraction? Or maybe I need to re-read the question.

The question says: “What is the mean, or average, number of shells collected?”

In many such worksheets, if it doesn’t divide evenly, they might accept the fraction or a decimal.

But let’s think — maybe I made a mistake in counting the X’s?

Wait — the user wrote:

“X X X” over 1 → 3
“X X” over 2 → 2
“X X X X” over 3 → 4
“X X X X X” over 4 → 5
“X X X” over 5 → 3

That’s 3+2+4+5+3=17, correct.

Sum: 1*3=3, 2*2=4, 3*4=12, 4*5=20, 5*3=15 → 3+4=7, 7+12=19, 19+20=39, 39+15=54.

So mean = 54/17.

But 54 ÷ 17 = 3.17647...

Perhaps for this level, they want it as a mixed number or rounded.

Looking at similar problems online, sometimes they expect the exact value.

But let me see — maybe I can write it as 3.18 if rounding to hundredths, but the problem doesn't specify.

Alternatively, perhaps I should leave it as a fraction.

But the blank is just a line — probably expects a number.

Another thought: did I misread the line plot? The user said "the line plot below shows", but since I can't see it, I relied on their description.

The user wrote:

"X X X" over 1
"X X" over 2
"X X X X" over 3
"X X X X X" over 4
"X X X" over 5

That seems clear.

Perhaps the mean is 54/17, but let's calculate it as a decimal for practicality.

54 ÷ 17 = 3.176... which rounds to 3.2 if to nearest tenth, or 3.18 to hundredths.

But in many school contexts, they might expect the fraction or the exact decimal.

Wait — let me check if 54 and 17 have common factors — 17 is prime, 54÷17 not integer, so fraction is 54/17.

But perhaps for the answer, I'll put the decimal rounded to two places, as it's common.

I recall that in some curricula, they teach to round mean to nearest tenth.

Let me assume that.

54 ÷ 17 = 3.176... → to nearest tenth is 3.2

But let's be precise.

Perhaps I should present it as 3.18, but I think for consistency, since other answers are integers, maybe they expect the calculation.

Another idea: perhaps I miscalculated the sum.

List all values:

Three 1's: 1,1,1 → sum 3
Two 2's: 2,2 → sum 4
Four 3's: 3,3,3,3 → sum 12
Five 4's: 4,4,4,4,4 → sum 20
Three 5's: 5,5,5 → sum 15

Total sum: 3+4=7; 7+12=19; 19+20=39; 39+15=54 — correct.

Number of items: 3+2+4+5+3=17 — correct.

So mean = 54/17.

But to match the format, perhaps write it as a decimal.

I think for this level, they might accept 3.2 or 3.18, but let's see the other answers are integers, so maybe I made a mistake.

Wait — let's count the X's again from the user's text:

"X X X" over 1 — that's 3
"X X" over 2 — 2
"X X X X" over 3 — 4
"X X X X X" over 4 — 5
"X X X" over 5 — 3

Yes.

Perhaps the "line plot" has different counts, but the user described it that way.

Maybe "X X X" means three, etc.

I think it's correct.

So for mean, I'll go with 54/17, but since the blank is for a number, and in many cases, they want the decimal, I'll calculate it as 3.18 if rounding to two decimals, but let's do exact.

Upon second thought, in the context of the worksheet, and since it's "median, mean, mode, range", and mode and median are integers, range is integer, total is integer, mean might be expected as a decimal.

Let me calculate 54 17:

17 * 3 = 51, remainder 3, so 3 + 3/17.

3/17 is approximately 0.176, so 3.176.

If we round to the nearest tenth, it's 3.2.

If to nearest hundredth, 3.18.

I think for school work, often they round to nearest tenth for mean.

Let me assume that.

So mean = 3.2

But to be accurate, let's see if there's a standard.

Perhaps the problem has a typo, but I doubt it.

Another approach: maybe I can leave it as a fraction, but the blank is probably for a number.

Looking at the response format, I need to provide final answer.

I think I'll go with the exact value as a decimal rounded to two places, as it's common.

So 54 ÷ 17 = 3.176470588... → rounded to two decimal places is 3.18

But let's confirm with calculation:

17 * 3.18 = 17*3 = 51, 17*0.18 = 3.06, total 54.06 — close to 54, a bit high.

17*3.17 = 17*3 = 51, 17*0.17 = 2.89, total 53.89 — closer to 54.

54 - 53.89 = 0.11, while 54.06 - 54 = 0.06, so 3.18 is closer? No:

17*3.17 = let's calculate: 10*3.17=31.7, 7*3.17=22.19, total 31.7+22.19=53.89

17*3.18 = 10*3.18=31.8, 7*3.18=22.26, total 54.06

54 - 53.89 = 0.11

54.06 - 54 = 0.06

So 3.18 gives 54.06, which is 0.06 over, while 3.17 gives 53.89, 0.11 under, so 3.18 is closer.

But actually, 54/17 = 3.17647..., so to two decimal places, look at third digit is 6>5, so round up 7 to 8, so 3.18.

Yes.

So mean = 3.18

But in some systems, they might want it as a fraction.

Given that, and to be safe, perhaps I should box the exact fraction, but I think for this context, decimal is fine.

Let's see the other questions — all answers are integers except possibly this.

Perhaps I can write it as 3.2 if rounding to tenths.

I recall that in many elementary stats, they round mean to nearest tenth.

For example, if it's 3.176, to nearest tenth is 3.2.

And 3.2 is simpler.

Let me check online or standard practice.

Since I can't, I'll go with 3.2 for simplicity, as it's commonly done.

Or perhaps the problem expects the calculation without rounding.

Another idea: maybe I miscounted the number of members.

Let's list the positions:

Data set sorted:

1,1,1,2,2,3,3,3,3,4,4,4,4,4,5,5,5

That's 17 numbers.

Position 9 is 3 (median), good.

Sum is 54.

Mean 54/17.

Perhaps in the answer, they want 54/17, but I think for the blank, it's a number.

I think I'll provide it as 3.18, but let's see the final answer format.

Perhaps for this worksheet, they have a specific expectation.

To resolve, let's calculate exactly.

I think for accuracy, I'll state it as 54/17, but since the instruction is to provide final answer, and it's a math problem, perhaps decimal is fine.

Let's look back at the user's request: "Solve the problem accurately."

So accurate is 54/17 or approximately 3.18.

But in the context, I think 3.18 is acceptable.

Perhaps they want it as a mixed number.

I recall that in some textbooks, they leave it as improper fraction.

But for this, I'll go with the decimal rounded to two places.

So mean = 3.18

But let's double-check the sum once more.

Values:

- 1 appears 3 times: contribution 3
- 2 appears 2 times: 4
- 3 appears 4 times: 12
- 4 appears 5 times: 20
- 5 appears 3 times: 15

3+4=7
7+12=19
19+20=39
39+15=54 — yes.

Number of data points: 3+2+4+5+3=17 — yes.

54 ÷ 17 = 3.176470588235294

Rounded to two decimal places: 3.18

Rounded to one decimal place: 3.2

I think for school work, one decimal place is sufficient for mean.

For example, if you have test scores, mean is often reported to one decimal.

So I'll go with 3.2

Let me decide: I'll use 3.2 for mean, as it's rounded to nearest tenth.

So:

1. Median: 3
2. Mode: 4
3. Range: 4
4. Total shells: 54
5. Mean: 3.2

But to be precise, let's see if the problem specifies.

It doesn't, so I'll use 3.2.

Perhaps the answer is 54/17, but I think for the blank, 3.2 is fine.

Another thought: in the line plot, maybe the X's are different, but based on user's description, it's correct.

I think I'm overthinking.

Let me proceed with the answers.

Final Answer:

1. 3
2. 4
3. 4
4. 54
5. 3.2

But for 5, to be accurate, perhaps write 54/17, but I think 3.2 is acceptable.

Let's calculate 54 ÷ 17 exactly: it's 3 and 3/17, and 3/17 is approximately 0.176, so 3.176, which to nearest tenth is 3.2.

Yes.

So I'll go with that.