Frequency Table worksheet - Free Printable

Explanation:
We are given a list of shoe sizes from a survey of students. Our job is to count how many times each shoe size appears (that’s the *frequency*), and then fill in the tally and frequency columns.

First, let’s list all the shoe sizes shown in the data:

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

Let’s count them one by one.

Shoe size 5:
Look through all rows:
- Row 1: two 5s
- Row 2: one 5
- Row 3: three 5s
- Row 4: two 5s
Total = 2 + 1 + 3 + 2 = 8

Shoe size 6:
- Row 1: three 6s
- Row 2: three 6s
- Row 3: two 6s
- Row 4: two 6s
Total = 3 + 3 + 2 + 2 = 10

Shoe size 7:
- Row 1: one 7
- Row 2: two 7s
- Row 3: two 7s
- Row 4: one 7
Total = 1 + 2 + 2 + 1 = 6

Shoe size 8:
- Row 1: one 8
- Row 2: one 8
- Row 4: one 8
Total = 1 + 1 + 1 = 3

Shoe size 9:
- Row 4: one 9
Total = 1

Now check total number of data points:
8 + 10 + 6 + 3 + 1 = 28
Let’s verify by counting total numbers in the grid: 4 rows × 7 numbers = 28 ✔️

Now convert frequencies to tallies:

- Frequency 8 → Tally: |||| |||| (or “|||| ||||” — but standard grouping is in fives: “|||| |” is 6, so 8 is “|||| |||” or better: “|||| ||||” — but usually we write as groups of 5: first 5 = |||||, next 3 = ||| → so “||||| |||”)
However, in the provided boxes, the tallies are shown as:
- III → 3
- |||| III → 8
- I → 1
- |||| |||| → 8? Wait — no, that’s 8 lines, but written as two groups of 4? Hmm — actually, the image shows 5 boxes with pre-drawn tallies:
1. III → 3
2. |||| III → that’s 4 + 3 = 7? Wait — careful: “||||” is 4, then “III” is 3 → total 7
But we have no size with frequency 7. Let's double-check our counts — maybe we made a mistake.

Let me recount more carefully, writing all values in a single list:

From the data:

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

Now count each:

Size 5: positions 5,7,12,17,18,20,23,28 → that’s 8 ✔
Size 6: 2,3,4,8,9,13,15,16,24,27 → that’s 10 ✔
Size 7: 6,10,14,19,21,25 → that’s 6 ✔
Size 8: 1,11,26 → that’s 3 ✔
Size 9: 22 → that’s 1 ✔

So frequencies are correct:
5 → 8
6 → 10
7 → 6
8 → 3
9 → 1

Now look at the tally boxes given:

Box 1: III → 3 → matches size 8
Box 2: |||| III → 4 + 3 = 7 → but we have no 7. Wait — maybe it's “||||| III” but printed poorly? Or maybe the formatting is: “|||| III” meaning 5 (|||||) is often written as four verticals and a diagonal, but here it's plain text.

Actually, in many worksheets, tally marks are grouped as:
- 1: I
- 2: II
- 3: III
- 4: IIII
- 5: |||| (with a diagonal slash) — but in plain text, they often write “||||” for 4, and “|||||” for 5, or sometimes “|||| /” — but here it's just lines.

The boxes show:
1. III → 3
2. |||| III → likely meant to be 8? Because 4 + 3 = 7, but maybe it's “||||| III” = 5+3=8 — but typed as “|||| III” missing one |.

Wait — look again: second box is “|||| III” — that’s 4 + 3 = 7 characters, but maybe it's a typo in rendering. However, the problem says: *Complete the tally chart below by dragging the correct box into the tally column* — meaning those 5 boxes are options to assign to the 5 rows.

So we need to match each frequency to one of these tally patterns:

Given tally options:
A: III → 3
B: |||| III → let's count the symbols: “||||” = 4, “III” = 3 → total 7
C: I → 1
D: |||| |||| → that’s 4 + 4 = 8
E: |||| I → 4 + 1 = 5

Wait — last one is “|||| I” — that’s 5.

But our frequencies are: 8, 10, 6, 3, 1.

We don’t have a tally for 10 or 6 in the options! That suggests maybe I misread the tally boxes.

Let me re-express the tally boxes exactly as shown in the prompt:

> [box] III
> [box] |||| III
> [box] I
> [box] |||| ||||
> [box] |||| I

Count characters (ignoring spaces):
1. III → 3
2. ||||III → 7 (if no space) — but there is a space, still 4 + 3 = 7
3. I → 1
4. |||||||| → 8
5. ||||I → 5

So tallies represent: 3, 7, 1, 8, 5

But our frequencies are: 5→8, 6→10, 7→6, 8→3, 9→1

Only matches:
- size 8 (freq 3) ↔ tally III
- size 9 (freq 1) ↔ tally I
- size 5 (freq 8) ↔ tally |||| |||| (8)
That leaves freq 10 and 6 unmatched — but we don’t have tallies for 10 or 6.

This implies: maybe I miscounted size 6?

Let me list all 28 values again, slowly:

Row 1: 8, 6, 6, 6, 5, 7, 5 → sizes: 8, six×3, five×2, seven×1
Row 2: 6, 6, 7, 8, 5, 6, 7 → six×3, seven×2, eight×1, five×1
Row 3: 6, 6, 5, 5, 7, 5, 7 → six×2, five×3, seven×2
Row 4: 9, 5, 6, 7, 8, 6, 5 → nine×1, five×2, six×2, seven×1, eight×1

Now sum per size:

Five: row1(2) + row2(1) + row3(3) + row4(2) = 8 ✔
Six: row1(3) + row2(3) + row3(2) + row4(2) = 10 ✔
Seven: row1(1) + row2(2) + row3(2) + row4(1) = 6 ✔
Eight: row1(1) + row2(1) + row4(1) = 3 ✔
Nine: row4(1) = 1 ✔

So frequencies are definitely 8, 10, 6, 3, 1.

But the tally options don’t include 10 or 6. Unless… the box “|||| III” is meant to be 8? No.

Wait — perhaps the second box is “||||| III” (5 + 3 = 8) but printed without the 5th | due to font? Unlikely.

Alternative: Maybe the teacher expects us to *create* the tally, not choose from boxes — but the instruction says: “by dragging the correct box into the tally column”.

Given this is a worksheet, and common tally groupings:
- 1: I
- 3: III
- 5: ||||| (or sometimes “|||| /”)
- 8: |||| |||| (two groups of 4) — but proper is group of 5: ||||| |||
- 10: two groups of 5: ||||| |||||
- 6: ||||| I

Looking at the boxes again:
- III = 3
- |||| III = possibly a misprint for “||||| III” = 8
- I = 1
- |||| |||| = 8 (but duplicate?)
- |||| I = 5

Wait — there are 5 boxes for 5 rows. We need tallies for frequencies: 1, 3, 6, 8, 10.

But none of the boxes is 6 or 10.

Unless… did we misread the data? Let me count total entries again: 4 rows × 7 = 28. Let’s count how many of each using a table:

Make a counter:
Start: {5:0, 6:0, 7:0, 8:0, 9:0}

Row 1: 8→+1, 6→+1 (x3), 5→+1 (x2), 7→+1
→ 5:2, 6:3, 7:1, 8:1

Row 2: 6,6,7,8,5,6,7
→ 6:+3 → total 6, 7:+2 → total 3, 8:+1 → 2, 5:+1 → 3

Row 3: 6,6,5,5,7,5,7
→ 6:+2 → 8, 5:+3 → 6, 7:+2 → 5

Row 4: 9,5,6,7,8,6,5
→ 9:+1, 5:+2 → 8, 6:+2 → 10, 7:+1 → 6, 8:+1 → 3

Final: 5:8, 6:10, 7:6, 8:3, 9:1 — confirmed.

Given that, and the tally options provided likely correspond as:

- Frequency 3 → III
- Frequency 1 → I
- Frequency 8 → |||| |||| (8 lines)
- Frequency 5 → |||| I (but we don’t have freq 5)
- Frequency 7 → |||| III (7)

But we don’t have freq 5 or 7. So the only logical conclusion: the tally boxes are meant to be assigned based on matching frequency, and perhaps the “|||| III” is actually 8 (if the first group is 5: “|||||” but written as “||||” by mistake), or the worksheet has a typo.

However, in many school worksheets, they use:
- 3: III
- 8: |||| III (meaning 5 + 3, and they write the 5 as four lines plus a slash, but in plain text it's shown as "|||| III" implying 5+3=8) — this is a common simplification.

Similarly:
- 10 would be “||||| |||||” — but not present.
- 6 would be “||||| I”

Wait — look at the fifth box: “|||| I” — that’s 5 marks? If “||||” is 4, plus “I” = 5. So that’s 5.

But we have no size with frequency 5.

Unless… did we miscount size 7? Let's list all 28 numbers and tally manually in a list:

Write them in order:
5,5,5,5,5,5,5,5 → that’s 8 fives
6,6,6,6,6,6,6,6,6,6 → 10 sixes
7,7,7,7,7,7 → 6 sevens
8,8,8 → 3 eights
9 → 1 nine

Yes.

Given the problem is designed for students, and the tally boxes are provided, the intended matching is likely:

- Shoes size 5 → frequency 8 → tally: |||| |||| (8 lines)
- Shoes size 6 → frequency 10 → but no tally for 10... unless the box “|||| III” is misread — wait, what if “|||| III” is actually 4 + 3 = 7, and maybe size 7 has frequency 7? Did we miscount 7?

Re-count sevens:
Positions with 7:
1. row1, col6
2. row2, col3
3. row2, col7
4. row3, col5
5. row3, col7
6. row4, col4
That’s 6.

No 7.

Perhaps the original data has a typo, but for the purpose of this task, the expected answer is based on correct counting, and the tally column should reflect the frequencies we found, regardless of the pre-drawn boxes (since the instruction also says “then complete the table by filling in the frequency” — so maybe the dragging is interactive, but for our answer, we just fill the table).

The question asks to complete the table with Tally and Frequency.

So let’s fill the table correctly:

Shoes Size | Tally | Frequency
5 | |||| |||| (or ||||| |||) | 8
6 | ||||| ||||| (two groups of 5) | 10
7 | ||||| I | 6
8 | III | 3
9 | I | 1

In standard tally notation:
- 8 = ||||| |||
- 10 = ||||| |||||
- 6 = ||||| I
- 3 = III
- 1 = I

Since the problem likely expects simple tally (group of 5 with a diagonal, but in text we use |), and for this format, we’ll write tallies as strings of |, grouped intuitively.

But the final answer should be the completed table.

Given the instructions, and that the student must fill the table, the correct frequencies are:

5 → 8
6 → 10
7 → 6
8 → 3
9 → 1

And tallies accordingly.

Since the question says “Complete the table by filling in the frequency”, and the tally can be derived, the key part is the frequency numbers.

Thus, the final answer is the frequency column values in order (size 5 to 9): 8, 10, 6, 3, 1.

But to be safe, let’s output the full completed table as answer.

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