Frequency Tables worksheet for students to practice creating tally charts and frequency tables from a list of shoe sizes.

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 match it with the correct tally marks.

First, let’s list all the numbers and count them one by one.

Shoe sizes we have: 5, 6, 7, 8, 9

Let’s go through the entire list and count each:

Start with size 5:
- Row 1: two 5s → positions 5 and 7
- Row 2: one 5 → position 5
- Row 3: three 5s → positions 3, 4, 6
- Row 4: two 5s → positions 2 and 7

Total for 5: 2 + 1 + 3 + 2 = 8

Now size 6:
- Row 1: three 6s → positions 2,3,4
- Row 2: four 6s? Wait — let’s check: positions 1,2,6 → that’s three? Wait no:

Wait, let me write out all values in order to avoid mistakes.

List all 28 numbers (4 rows × 7 columns):

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

Now let’s list them all in one line:

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

Now count each size carefully.

Size 5: Let’s find every “5”

Positions (counting from start):
5th, 7th, 12th, 17th, 18th, 20th, 23rd, 28th → that’s 8 fives.

Yes, 8.

Size 6: Find every “6”

2nd, 3rd, 4th, 8th, 9th, 13th, 15th, 16th, 24th, 26th → let’s count:

From row1: 3 sixes (positions 2,3,4)
Row2: positions 1,2,6 → that’s 3 more → total 6
Row3: positions 1,2 → that’s 2 more → total 8
Row4: positions 3,6 → that’s 2 more → total 10

Wait — let’s list indices:

Full list index (1-based):

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

So 6s at: 2,3,4,8,9,13,15,16,24,27 → that’s 10 sixes.

Yes, 10.

Size 7: Find every “7”

6th, 10th, 14th, 19th, 21st, 25th → and also?

Row1: position 6 → 7
Row2: positions 3,7 → 7,7
Row3: positions 5,7 → 7,7
Row4: position 4 → 7

So: 6,10,14,19,21,25 → that’s 6 sevens? Wait:

Index 6:7
Index 10:7
Index 14:7
Index 19:7
Index 21:7
Index 25:7 → yes, 6 sevens.

But wait — row2 has two 7s? Index 10 and 14? Let’s see:

After row1 (7 items), row2 starts at index 8:

Index 8:6
9:6
10:7 ←
11:8
12:5
13:6
14:7 ← → yes

Row3: index 15:6, 16:6, 17:5, 18:5, 19:7 ←, 20:5, 21:7 ←

Row4: index 22:9, 23:5, 24:6, 25:7 ←, 26:8, 27:6, 28:5

So 7s at: 6,10,14,19,21,25 → that’s 6.

Wait — is there another? Row3 has two 7s? Yes, 19 and 21. Row4 has one at 25. Row2 has two at 10 and 14. Row1 has one at 6. Total: 1+2+2+1=6. Correct.

Size 8: Find every “8”

Index 1:8
Index 11:8
Index 26:8 → that’s three 8s.

Row1: first number is 8
Row2: fourth number is 8 (index 11)
Row4: fifth number is 8 (index 26)

Yes, 3 eights.

Size 9: Only one — index 22:9

So summary:

Size 5: 8
Size 6: 10
Size 7: 6
Size 8: 3
Size 9: 1

Now look at the tally boxes provided:

The boxes show:

Box A: III → that’s 3
Box B: HHH III → that’s 5 + 3 = 8? Wait, standard tally: each group of 5 is four lines and a diagonal. But here they wrote "HHH" which might mean five? Actually, looking at the image description, it says:

Boxes:
- III → 3
- HHH III → probably means two groups: first group of 5 (represented as HHH? That doesn’t make sense). Wait, perhaps it's a typo or misrendering.

Actually, in the user’s message, it says:

“Complete the tally chart below by dragging the correct box into the tally column”

And the boxes are:

||| , |||| ||| , | , |||| |||| , |||| |

Ah! Probably it’s meant to be tally marks using vertical bars.

In text, sometimes “||||” represents four, and “|||| |” is five, etc.

Looking back:

The boxes are described as:

- III → that’s three vertical lines → 3
- HHH III → likely meant to be “|||| |||” → that would be 5 + 3 = 8? But “HHH” isn't standard.

Wait, in the original problem statement, it says:

“dragging the correct box into the tally column”

And the boxes are shown as:

[ ||| ] [ |||| ||| ] [ | ] [ |||| |||| ] [ |||| | ]

I think “HHH” was a formatting error — it should be vertical bars.

Assuming:

Box 1: ||| → 3
Box 2: |||| ||| → that’s 4 + 3 = 7? Or if “||||” is a group of 5? No, standard tally: a group of 5 is four vertical and one diagonal, but in plain text, often written as “|||| |” for 5, “|||| ||” for 6, etc.

But in the boxes given:

It says:

“III” → 3
“HHH III” — probably “|||| |||” meaning 5 + 3 = 8? But “HHH” might be a mistake for “||||” (four lines) but that doesn’t add up.

Wait, let’s read the user input again:

“Complete the tally chart below by dragging the correct box into the tally column and then complete the table by filling in the frequency.”

Then it shows:

[ ||| ] [ |||| ||| ] [ | ] [ |||| |||| ] [ |||| | ]

I think “HHH” was a typo and should be “||||”.

So interpreting:

Box A: ||| → 3
Box B: |||| ||| → if “||||” is 4 and “|||” is 3, total 7? But that doesn’t match our counts.

Perhaps “||||” represents a group of 5? In some notations, but usually not.

Another possibility: in the image, the tallies are drawn properly, but in text, it’s misrepresented.

Given the frequencies we calculated:

Size 5: 8 → needs tally for 8
Size 6: 10 → tally for 10
Size 7: 6 → tally for 6
Size 8: 3 → tally for 3
Size 9: 1 → tally for 1

Now look at the available tally boxes:

From the description:

Boxes:
1. ||| → 3
2. |||| ||| → let’s assume this is 5 + 3 = 8? If “||||” is a group of 5 (with diagonal), but in text it’s hard.

Perhaps the second box is “|||| |||” meaning two groups: first group 5, second group 3, total 8.

Similarly, fourth box: “|||| ||||” → two groups of 5? 10.

Fifth box: “|||| |” → 5 + 1 = 6

Third box: “|” → 1

First box: “|||” → 3

That makes sense!

So:

- ||| → 3
- |||| ||| → 5 + 3 = 8
- | → 1
- |||| |||| → 5 + 5 = 10
- |||| | → 5 + 1 = 6

Perfect! Matches our frequencies.

So now assign:

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

Now fill the table.

Final Answer:

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

Note: The tally marks are represented as groups where "||||" stands for a group of 5 (though typically it's four vertical and one diagonal, in text we use this notation).

So the completed table is as above.