Dot Plots | Worksheet - Free Printable

Let’s solve each problem step by step.

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Problem 1: Dice Rolls Dot Plot

We are given a list of dice rolls from 25 turns:

Numbers Rolled:
3, 6, 1, 6, 4,
2, 5, 1, 4, 6,
2, 6, 5, 3, 1,
2, 4, 5, 6, 3,
1, 3, 4, 4, 3

We need to count how many times each number (1 through 6) appears. Then we’ll place that many dots above each number on the dot plot.

Let’s count:

- Number 1: appears in positions: row1-col3, row2-col3, row3-col5, row5-col1 → that’s 4 times
Wait — let me go slowly and list all occurrences:

Go through each number one by one:

List again for clarity:

Row 1: 3, 6, 1, 6, 4
Row 2: 2, 5, 1, 4, 6
Row 3: 2, 6, 5, 3, 1
Row 4: 2, 4, 5, 6, 3
Row 5: 1, 3, 4, 4, 3

Now count each digit:

→ 1: Row1-col3, Row2-col3, Row3-col5, Row5-col1 → 4 times

→ 2: Row2-col1, Row3-col1, Row4-col1 → 3 times

→ 3: Row1-col1, Row3-col4, Row4-col5, Row5-col2, Row5-col5 → 5 times

Wait — Row1-col1 is 3? Yes. Row3-col4 is 3? Yes. Row4-col5 is 3? Yes. Row5-col2 is 3? Yes. Row5-col5 is 3? Yes. That’s 5.

But wait — let me write them out:

Positions with 3:
- First number: 3
- Third row, fourth number: 3
- Fourth row, fifth number: 3
- Fifth row, second number: 3
- Fifth row, fifth number: 3 → yes, 5 threes.

→ 4: Row1-col5, Row2-col4, Row4-col2, Row5-col3, Row5-col4 → that’s 5 fours? Let’s check:

Row1: last is 4 → 1
Row2: fourth is 4 → 2
Row4: second is 4 → 3
Row5: third and fourth are both 4 → 4 and 5 → total 5

→ 5: Row2-col2, Row3-col3, Row4-col3 → that’s 3 fives? Wait:

Row2: second is 5 → 1
Row3: third is 5 → 2
Row4: third is 5 → 3
Any others? No → 3

→ 6: Row1-col2, Row1-col4, Row2-col5, Row3-col2, Row4-col4 → that’s 5 sixes?

Row1: second and fourth → 2
Row2: fifth → 3
Row3: second → 4
Row4: fourth → 5 → yes, 5

Wait — let’s add up totals to make sure we have 25:

1: 4
2: 3
3: 5
4: 5
5: 3
6: 5
Total = 4+3=7; +5=12; +5=17; +3=20; +5=25 → perfect.

So frequencies:

Number | Frequency
1 | 4
2 | 3
3 | 5
4 | 5
5 | 3
6 | 5

On the dot plot, for each number on the x-axis (“Number Rolled”), we put that many dots above it.

For example, above “1” we put 4 dots stacked vertically. Above “2” we put 3 dots, etc.

The current dot plot already has one green dot above “5” — but that must be a placeholder or error? Because according to our count, 5 should have 3 dots. But since the instruction says “the first dot has been plotted for you”, maybe they meant to start us off — but actually looking at the image description, it shows a single green dot above 5. However, based on data, 5 occurs 3 times, so we need 3 dots above 5.

But perhaps the green dot is just an example and not part of the actual data? The problem says “the first dot has been plotted for you” — but doesn’t specify which number. In the text, it might be misleading. Since we’re solving based on data, we ignore any pre-plotted dots unless instructed otherwise. Actually, re-reading: “Use the key to create a dot plot. The first dot has been plotted for you.” But in the provided table, there's no key shown — probably in original worksheet there was a key. Since we don’t have it, and the data is clear, we proceed with counts.

Actually, looking back — in the user’s image description, under “Dice Rolls” dot plot, there is already one green dot above 5. But according to our count, 5 appears 3 times. So if one is already there, we need to add 2 more? Or is that dot incorrect?

Wait — perhaps I miscounted. Let me double-check the dice rolls.

Given numbers:

Line 1: 3, 6, 1, 6, 4 → that’s five numbers
Line 2: 2, 5, 1, 4, 6
Line 3: 2, 6, 5, 3, 1
Line 4: 2, 4, 5, 6, 3
Line 5: 1, 3, 4, 4, 3

Let me tally using a frequency counter:

Start with zeros:

1: 0
2: 0
3: 0
4: 0
5: 0
6: 0

Go line by line:

Line 1: 3→3++, 6→6++, 1→1++, 6→6++, 4→4++
Now: 1:1, 3:1, 4:1, 6:2

Line 2: 2→2++, 5→5++, 1→1++, 4→4++, 6→6++
Now: 1:2, 2:1, 3:1, 4:2, 5:1, 6:3

Line 3: 2→2++, 6→6++, 5→5++, 3→3++, 1→1++
Now: 1:3, 2:2, 3:2, 4:2, 5:2, 6:4

Line 4: 2→2++, 4→4++, 5→5++, 6→6++, 3→3++
Now: 1:3, 2:3, 3:3, 4:3, 5:3, 6:5

Line 5: 1→1++, 3→3++, 4→4++, 4→4++, 3→3++
Now: 1:4, 2:3, 3:5, 4:5, 5:3, 6:5

Yes! Confirmed:

1: 4
2: 3
3: 5
4: 5
5: 3
6: 5

So for the dot plot:

Above 1: 4 dots
Above 2: 3 dots
Above 3: 5 dots
Above 4: 5 dots
Above 5: 3 dots
Above 6: 5 dots

If the problem says “the first dot has been plotted for you”, and in the image there’s a dot above 5, then perhaps we only need to add 2 more dots above 5, and full sets for others. But since the instruction is to “use the key to create a dot plot”, and we don’t have the key, and the data is clear, I think we are to complete the entire plot based on data. Maybe the green dot is just illustrative. To be safe, I’ll assume we need to show the correct number of dots for each, regardless of any pre-existing dot.

But since this is a text-based response, I can't draw dots. So I will describe what the completed dot plot should look like.

Alternatively, perhaps the question expects us to fill in the missing dots. Given that, and since the problem says “the first dot has been plotted for you”, and assuming that dot is above 5 (as per typical layout), then for number 5, we already have 1 dot, so we need to add 2 more. For all other numbers, we add the full count.

But without seeing the exact image, it’s ambiguous. However, in standard problems like this, when they say “first dot plotted”, it’s often to show the format, and you complete the rest. Since 5 has frequency 3, and one is already there, we add two more above 5. For others, we add all.

But to avoid confusion, and since the main goal is to understand the frequency, I’ll state the required dots per number.

Perhaps better: the answer is to have the following number of dots above each number:

- 1: ●●●● (4 dots)
- 2: ●●● (3 dots)
- 3: ●●●●● (5 dots)
- 4: ●●●●● (5 dots)
- 5: ●●● (3 dots) — if one is already there, add two more
- 6: ●●●●● (5 dots)

Since the problem likely expects the student to add dots to the plot, and we can't draw here, I'll note the counts.

But for Final Answer, perhaps they want the completed plot described or the frequencies. Looking at the context, since it's a worksheet, the answer is the dot plot with correct dots. But as text, I'll summarize.

Moving to Problem 2.

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Problem 2: Fitness Class Chin-ups

Frequency table:

Number of Chin-ups | Number of People
6 | 3
7 | ?
8 | ?
9 | ?
10 | ?

And the data set is given as a list:

Data: 8, 9, 6, 10, 7, 8, 6, 6, 8, 9, 7, 8, 6, 8, 7, 9, 8, 10, 8, 7

We need to count how many people did each number of chin-ups, then fill in the frequency table, then create a dot plot.

First, let’s list all the data points clearly:

From the string: "8, 9, 6, 10, 7, 8, 6, 6, 8, 9, 7, 8, 6, 8, 7, 9, 8, 10, 8, 7"

That’s 20 numbers.

Count frequency for each chin-up count:

Make a tally:

Start with 6: appears how many times?

Look: positions with 6: 3rd, 7th, 8th, 13th → that’s four 6s? Let’s list indices:

Write the sequence:

1:8, 2:9, 3:6, 4:10, 5:7, 6:8, 7:6, 8:6, 9:8, 10:9, 11:7, 12:8, 13:6, 14:8, 15:7, 16:9, 17:8, 18:10, 19:8, 20:7

Now count:

→ 6: positions 3,7,8,13 → that’s 4 times

→ 7: positions 5,11,15,20 → and also position 5,11,15,20 — that’s 4? Wait, position 5:7, 11:7, 15:7, 20:7 → yes 4. But is there more? Position 5,11,15,20 — that’s four. What about others? No, only those. But let me check: after 15 is 16:9, 17:8, 18:10, 19:8, 20:7 — yes, only four 7s? Wait, earlier I thought more.

List all 7s:

- Index 5: 7
- Index 11: 7
- Index 15: 7
- Index 20: 7
That’s 4.

But wait, in the data: "8, 9, 6, 10, 7, 8, 6, 6, 8, 9, 7, 8, 6, 8, 7, 9, 8, 10, 8, 7" — let's group:

After "10," is "7" (5th), then later "7" (11th), then "7" (15th), then "7" (20th) — yes, four.

→ 8: let's count: indices 1,6,9,12,14,17,19 — and also? 1:8, 6:8, 9:8, 12:8, 14:8, 17:8, 19:8 — that’s seven? Wait, index 1,6,9,12,14,17,19 — that's 7 eights.

Is there more? Index 1,6,9,12,14,17,19 — yes 7.

But let's list: 1st:8, 6th:8, 9th:8, 12th:8, 14th:8, 17th:8, 19th:8 — that's 7.

→ 9: indices 2,10,16 — that's three 9s? 2nd:9, 10th:9, 16th:9 — yes 3.

→ 10: indices 4,18 — that's two 10s.

Now verify total: 6s:4, 7s:4, 8s:7, 9s:3, 10s:2 → 4+4=8; +7=15; +3=18; +2=20 — perfect.

So frequency table should be:

Number of Chin-ups | Number of People
6 | 4
7 | 4
8 | 7
9 | 3
10 | 2

In the given table, for 6 it says 3, but we counted 4. Probably a typo in the problem or in my reading? Let me check the data again.

The data is: "8, 9, 6, 10, 7, 8, 6, 6, 8, 9, 7, 8, 6, 8, 7, 9, 8, 10, 8, 7"

Count 6s: third item is 6, seventh is 6, eighth is 6, thirteenth is 6 — that's four 6s. But the table says for 6: 3. That must be a mistake in the worksheet, or perhaps I misread.

Looking back at user's input: "Fitness Class Chin-ups" table shows:

Number of Chin-ups | Number of People
6 | 3
7 |
8 |
9 |
10 |

But according to data, it should be 4 for 6. Perhaps the data has only three 6s? Let me recount the data string.

User wrote: "8, 9, 6, 10, 7, 8, 6, 6, 8, 9, 7, 8, 6, 8, 7, 9, 8, 10, 8, 7"

Let's split by commas:

1. 8
2. 9
3. 6
4. 10
5. 7
6. 8
7. 6
8. 6
9. 8
10. 9
11. 7
12. 8
13. 6
14. 8
15. 7
16. 9
17. 8
18. 10
19. 8
20. 7

6s at positions 3,7,8,13 — that's four. But the table says 3 for 6. This is inconsistent.

Perhaps the "3" is a placeholder or error. Or maybe I need to use the data as is. Another possibility: the table is partially filled, and "3" for 6 is correct, but then the data must have only three 6s. But it has four.

Unless the data is different. Let me read the user's input carefully: "the number of chin-ups completed by each person is listed below. Use the key to fill in the frequency table."

And the list is: "8, 9, 6, 10, 7, 8, 6, 6, 8, 9, 7, 8, 6, 8, 7, 9, 8, 10, 8, 7"

Perhaps the first "6" is not there? No, it's there.

Maybe the table's "3" for 6 is a mistake, and we should correct it. In educational contexts, sometimes worksheets have errors, but we go by the data.

To resolve, I'll assume the data is correct, so frequency for 6 is 4, not 3. Perhaps the "3" is for another number, but it's written under 6.

Another idea: perhaps the table is to be filled, and the "3" is an example or something, but it's under 6.

Looking at the structure, in the dice roll problem, the table had data, and we counted. Here, the table has "3" for 6, but data shows 4. I think it's likely a typo, and we should use the data.

Perhaps "Number of People" for 6 is given as 3, but that contradicts data. I think for accuracy, we use the data provided.

So I'll proceed with:

6: 4
7: 4
8: 7
9: 3
10: 2

Then for the dot plot, above each number on x-axis ("Number of Chin-ups"), we put that many dots.

For example, above 6: 4 dots, above 7: 4 dots, etc.

Again, since we can't draw, we describe.

But for the final answer, since the problem asks to "fill in the frequency table" and "create a dot plot", and we're to provide the answer, I'll state the completed frequency table and the dot counts.

Perhaps the expected answer is the filled table.

Let me see the options: the user didn't specify what to output, but since it's homework, likely the completed tables or plots.

But in text, I'll summarize.

For Problem 1, the dot plot should have:

- 1: 4 dots
- 2: 3 dots
- 3: 5 dots
- 4: 5 dots
- 5: 3 dots
- 6: 5 dots

For Problem 2, the frequency table should be:

Number of Chin-ups | Number of People
6 | 4
7 | 4
8 | 7
9 | 3
10 | 2

And dot plot accordingly.

But to match the worksheet, for Problem 2, if the table already has 3 for 6, perhaps we leave it, but that would be wrong. I think we correct it.

Perhaps the data has 20 entries, and if 6 is 3, then others adjust, but no, counting shows 4.

Another thought: in the data string, is "6, 6, 8" etc., but let's count the 6s explicitly:

From the list: after "9," is "6" (first 6), then later "6, 6" (seventh and eighth), then "6" (thirteenth) — so four times.

I think it's safe to go with data.

So for Final Answer, I'll provide the completed frequency distributions.

Since the problem might expect the dot plot descriptions, but as text, I'll box the frequencies.

Perhaps for each problem, the answer is the set of frequencies.

Let's finalize.

For Problem 1: Frequencies for dice rolls: 1:4, 2:3, 3:5, 4:5, 5:3, 6:5

For Problem 2: Frequencies for chin-ups: 6:4, 7:4, 8:7, 9:3, 10:2

And for the dot plots, those are the number of dots to place.

So in the response, I'll state that.

Final Answer will be the completed tables or the dot counts.

Since the user said "solve the problem accurately", and problems are to create dot plots, but in text, I'll provide the frequency counts which define the dot plots.

So for Problem 1, the dot plot has the following number of dots for each number rolled:

- 1: 4
- 2: 3
- 3: 5
- 4: 5
- 5: 3
- 6: 5

For Problem 2, the frequency table is filled as:

- 6 chin-ups: 4 people
- 7 chin-ups: 4 people
- 8 chin-ups: 7 people
- 9 chin-ups: 3 people
- 10 chin-ups: 2 people

And the dot plot reflects these frequencies.

I think that's the solution.

Now for the Final Answer section, since there are two problems, I'll combine.

Perhaps write:

For the dice rolls dot plot, the number of dots above each number is: 1→4, 2→3, 3→5, 4→5, 5→3, 6→5.

For the fitness class, the completed frequency table is: 6:4, 7:4, 8:7, 9:3, 10:2.

So in boxed, I'll put that.

But to be precise.