Frequency Table worksheet - Free Printable

Let’s solve this step by step.

We are given a list of shoe sizes from students:

Row 1: 8, 6, 6, 6, 5, 7, 5
Row 2: 6, 6, 7, 8, 5, 6, 7
Row 3: 6, 6, 5, 5, 7, 5, 7
Row 4: 9, 5, 6, 7, 8, 6, 5

We need to count how many times each shoe size appears (that’s the frequency), and then write it using tally marks.

Tally marks work like this:
- Each mark is one count: |
- After four vertical lines, the fifth is drawn diagonally across them: |||| → that’s 5.
- So for example, 7 would be: |||| || (five + two)
- 8 would be: |||| ||| (five + three)
- 9 would be: |||| |||| (five + four) — but wait, actually, we usually do groups of five. Let me double-check standard tallying.

Actually, standard tallying:
- 1 = |
- 2 = ||
- 3 = |||
- 4 = ||||
- 5 = ||||\ (a diagonal line through the first four)
- 6 = ||||\ |
- 7 = ||||\ ||
- 8 = ||||\ |||
- 9 = ||||\ ||||
- 10 = ||||\ ||||\ (two groups of five)

But in the image, they show examples like:
- “III” → that’s 3
- “|||| III” → that’s 5 + 3 = 8? Wait, no — looking at the boxes provided:

The draggable boxes are:
Box 1: III → 3
Box 2: |||| III → that’s 5 + 3 = 8? But written as “|||| III” — maybe they mean 4 vertical and then 3 more? That doesn’t follow standard grouping. Actually, let’s look again.

Wait — in the problem, the boxes shown are:

First box: "III" → 3
Second box: "|||| III" → probably meant to be 5 (as a group) plus 3? But written without the slash? Hmm.

Actually, looking carefully at the image description (even though I can't see it, based on your text):

You wrote:
> Complete the tally chart below by dragging the correct box into the tally column...

And the boxes are:
- Box A: III → 3
- Box B: |||| III → likely 8? Because 4 vertical + 3 more = 7? No — if “||||” is 4, and “III” is 3, together 7? But that’s not grouped.

Wait — perhaps the notation here is non-standard. Let me re-read:

In the user's message, the boxes are described as:

“|||” , “|||| III”, “|”, “|||| ||||”, “|||| I”

Ah! Now I see — these are meant to represent tallies with groups of five implied by “||||” meaning a full group of 5? Or is “||||” just 4?

This is confusing. Let me think differently.

Standard tally marks use a diagonal line for every fifth mark. But in some worksheets, especially for younger students, they might just write vertical lines and group them visually.

Looking at the options given in the problem (from your text):

The available tally boxes are:
1. III → 3
2. |||| III → this looks like 4 + 3 = 7? Or if “||||” represents 5, then 5+3=8? But that’s inconsistent.

Wait — another possibility: In some systems, “||||” is used to mean 5 (with an implied diagonal), and then additional marks are added. But in plain text, it’s hard.

Perhaps the intended interpretation is:

- “I” = 1
- “II” = 2
- “III” = 3
- “IIII” = 4
- “IIII I” = 5? No, that doesn’t make sense.

Let me count the actual frequencies first from the data, then match to the closest tally representation.

List all shoe sizes:

From Row 1: 8,6,6,6,5,7,5 → sizes: 5,5,6,6,6,7,8
Row 2: 6,6,7,8,5,6,7 → 5,6,6,6,7,7,8
Row 3: 6,6,5,5,7,5,7 → 5,5,5,6,6,7,7
Row 4: 9,5,6,7,8,6,5 → 5,5,6,6,7,8,9

Now let’s count each size:

Size 5:
Row1: two 5s
Row2: one 5
Row3: three 5s
Row4: two 5s
Total: 2+1+3+2 = 8

Size 6:
Row1: three 6s
Row2: three 6s (positions: first, second, sixth) → yes, 6,6,7,8,5,6,7 → so 6 appears at index 1,2,6 → three times
Row3: two 6s (first two: 6,6,...)
Row4: two 6s (third and sixth: 9,5,6,7,8,6,5 → positions 3 and 6)
So: 3 + 3 + 2 + 2 = 10

Wait, let me list all numbers explicitly to avoid error.

Write all 28 numbers in order:

Row1: 8,6,6,6,5,7,5 → [8,6,6,6,5,7,5]
Row2: 6,6,7,8,5,6,7 → [6,6,7,8,5,6,7]
Row3: 6,6,5,5,7,5,7 → [6,6,5,5,7,5,7]
Row4: 9,5,6,7,8,6,5 → [9,5,6,7,8,6,5]

Now combine into one list:

[8,6,6,6,5,7,5, 6,6,7,8,5,6,7, 6,6,5,5,7,5,7, 9,5,6,7,8,6,5]

Count occurrences:

Size 5: let's go through the list:

Position 5:5, pos7:5, pos12:5, pos17:5, pos18:5, pos20:5, pos23:5, pos28:5 → that’s 8 fives.

List indices (1-based):

1:8
2:6
3:6
4:6
5:5 ←1
6:7
7:5 ←2
8:6
9:6
10:7
11:8
12:5 ←3
13:6
14:7
15:6
16:6
17:5 ←4
18:5 ←5
19:7
20:5 ←6
21:7
22:9
23:5 ←7
24:6
25:7
26:8
27:6
28:5 ←8

Yes, size 5 appears 8 times.

Size 6:

Positions: 2,3,4,8,9,13,15,16,24,27 → that’s 10 sixes.

Check: 2,3,4 (three), 8,9 (two more → five), 13 (sixth), 15,16 (eighth), 24 (ninth), 27 (tenth). Yes, 10.

Size 7:

Positions: 6,10,14,19,21,25 → that’s 6 sevens.

List: 6,10,14,19,21,25 → yes, six.

Size 8:

Positions: 1,11,26 → that’s three eights.

Also position ? Row1 first is 8, row2 fourth is 8, row4 sixth is 8 → yes, three.

Size 9:

Only position 22 → one nine.

So summary:

Shoe Size | Frequency
5 | 8
6 | 10
7 | 6
8 | 3
9 | 1

Now, we need to represent these frequencies with tally marks using the provided boxes.

The available tally boxes are (from your description):

Box A: "III" → 3
Box B: "|||| III" → this must be 8? Because 5 + 3 = 8? If "||||" represents a group of 5, then "|||| III" is 5+3=8.
Box C: "|" → 1
Box D: "|||| ||||" → if each "||||" is 5, then 5+5=10? But written as two groups of four? That doesn’t make sense. Perhaps "|||| ||||" means 8? But we already have Box B for 8.

Wait — let's interpret the boxes as they are written in plain text:

- "III" = three vertical lines → 3
- "|||| III" = four vertical + three vertical = 7? But that would be unusual.
Alternatively, perhaps "||||" is meant to be a group of 5 (with an implied diagonal), so "|||| III" = 5 + 3 = 8
Similarly, "|||| ||||" = 5 + 5 = 10? But written as two sets of four? That’s inconsistent.

Another possibility: in some contexts, especially in digital formats, they use "IIII" for 4, and then add more, but for 5, they might use "IIIII" or something else.

But looking at the last box: "|||| I" → if "||||" is 4, then +1 = 5? Or if "||||" is 5, then +1=6.

This is ambiguous. However, since we have specific frequencies, and only certain boxes, let's map:

We need tallies for:
- 5: freq 8 → needs a tally representing 8
- 6: freq 10 → needs 10
- 7: freq 6 → needs 6
- 8: freq 3 → needs 3
- 9: freq 1 → needs 1

Available boxes:
1. "III" → 3 → perfect for size 8 (freq 3)
2. "|||| III" → if this is 8, then good for size 5 (freq 8)
3. "|" → 1 → good for size 9 (freq 1)
4. "|||| ||||" → if this is 10 (two groups of 5), then good for size 6 (freq 10)
5. "|||| I" → if "||||" is 5, then +1=6 → good for size 7 (freq 6)

That makes sense!

So interpreting:
- "III" = 3
- "|||| III" = 5 + 3 = 8 (assuming "||||" represents a group of 5)
- "|" = 1
- "|||| ||||" = 5 + 5 = 10
- "|||| I" = 5 + 1 = 6

Even though in standard notation, a group of 5 is shown with a diagonal, in this worksheet, they are using "||||" to mean 5, and then adding extra marks.

So assignment:

Shoe Size 5 → frequency 8 → tally: "|||| III"
Shoe Size 6 → frequency 10 → tally: "|||| ||||"
Shoe Size 7 → frequency 6 → tally: "|||| I"
Shoe Size 8 → frequency 3 → tally: "III"
Shoe Size 9 → frequency 1 → tally: "|"

Now, fill the table:

Shoes Size | Tally | Frequency
5 | |||| III | 8
6 | |||| |||| | 10
7 | |||| I | 6
8 | III | 3
9 | | | 1

Double-check counts:

Total students: 8+10+6+3+1 = 28, which matches the number of data points (4 rows × 7 = 28). Good.

Final Answer:

Shoes Size | Tally | Frequency
5 | |||| III | 8
6 | |||| |||| | 10
7 | |||| I | 6
8 | III | 3
9 | | | 1