Math worksheet for creating line plots from book height data.

Let’s solve this step by step.

We are given two tables with book heights in inches and tally marks. We need to:

1. Fill in the frequency column (count how many tally marks for each height).
2. Use that data to answer questions 3–7.
3. (Optionally) complete the line plot — but since we’re not drawing, we’ll just use the numbers.

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Step 1: Count frequencies from tallies

Remember:
- Each vertical line “|” = 1
- A group of 5 is shown as four lines with a diagonal slash through them: “||||” with a slash = 5
- So “|||| |||” means 5 + 3 = 8

#### Left Table:

| Height (inches) | Tally | Frequency |
|------------------|-----------|---------|
| 5 | II | 2 | ← already filled
| 5¼ | I | 1 |
| 5½ | IIII | 4 | ← wait! That’s only 4? But usually “IIII” without slash is 4. However, looking at next row...
Wait — let me check again.

Actually, looking carefully:

In the left table:

- 5 → II → 2 ✔️
- 5¼ → I → 1
- 5½ → IIII → that’s 4? But sometimes people write 5 as IIII with a slash. Here it’s written as “IIII” — no slash? Wait, in the image description, it says:

> 5½ → IIII
> 5¾ → IIII
> 6 → IIII III → which is 5 + 3 = 8

Ah — so “IIII” alone likely means 4? But that would be unusual. Let me re-express based on standard tallying:

Standard tally: every 5th mark crosses the previous 4.

So if it says:

- “II” = 2
- “I” = 1
- “IIII” = 4? Or is it meant to be 5?

Wait — look at row for 6: “IIII III” — that’s clearly 5 + 3 = 8.

Similarly, row for 7: “IIII II” — that’s 5 + 2 = 7.

So yes — “IIII” with a slash implied? Actually, in text, they might write “IIII” to mean 5? No — that doesn’t make sense.

Wait — let's read the original problem again.

From user input:

Left table:

HEIGHT | TALLY | FREQUENCY
5 | II | 2
5¼ | I | ?
5½ | IIII | ?
5¾ | IIII | ?
6 | IIII III | ?

Right table:

6¼ | II | ?
6½ | IIII | ?
6¾ | II | ?
7 | IIII II | ?
7¼ | I | ?

Now, note: For 6, it says “IIII III” — that’s 5 + 3 = 8.

For 7, “IIII II” — 5 + 2 = 7.

So “IIII” by itself must mean 4? But that contradicts standard tallying where 5 is grouped.

Wait — perhaps there’s a typo in interpretation.

Actually, in many worksheets, when they write “IIII” without a slash, they still mean 4, and “IIII /” or similar means 5. But here, for 6, it’s written as “IIII III” — meaning first group of 5 (written as IIII with an implied slash?) plus 3 more.

But in text, it’s hard to show the slash. So likely:

- “IIII” = 4? But then 6 has “IIII III” = 4 + 3 = 7? But that doesn’t match because 6 should be higher.

Wait — let’s count total books later to verify.

Alternative approach: Assume that whenever you see “IIII”, it represents 5, even if no slash is drawn in text. Because otherwise the numbers don’t add up reasonably.

Look at 6: “IIII III” — if “IIII” = 5, then 5 + 3 = 8.

Similarly, 7: “IIII II” = 5 + 2 = 7.

Then 5½: “IIII” = 5? But that would be inconsistent because 5¼ is “I” = 1, 5 is “II” = 2.

Wait — let’s list all tallies as written:

Left table:

- 5: II → 2
- 5¼: I → 1
- 5½: IIII → let’s assume this is 4? Or 5?
- 5¾: IIII → same
- 6: IIII III → 5 + 3 = 8

If “IIII” = 4, then 5½ = 4, 5¾ = 4, 6 = 4 + 3 = 7? But that seems low.

But look at right table:

- 6¼: II → 2
- 6½: IIII → 4 or 5?
- 6¾: II → 2
- 7: IIII II → 5 + 2 = 7
- 7¼: I → 1

Also, question 5 asks: “How many more books are 7 inches tall than 6¾ inches tall?”

If 7 is 7 books, and 6¾ is 2, then difference is 5 — that makes sense.

Similarly, question 4: tallest minus shortest.

Shortest is 5 inches (2 books), tallest is 7¼ (1 book)? Or 7? 7¼ is taller.

Height goes up to 7¼.

So tallest is 7¼, shortest is 5.

Difference: 7¼ - 5 = 2¼ inches.

That seems reasonable.

Now back to frequencies.

I think the key is: in the tally column, “IIII” means 4, and “IIII III” means 4 + 3 = 7? But that contradicts standard practice.

Wait — let’s look at the example given: for height 5, tally is “II”, frequency is 2 — correct.

For height 6, tally is “IIII III” — if we interpret “IIII” as 4 and “III” as 3, total 7.

But then for height 7, “IIII II” = 4 + 2 = 6.

But earlier I thought 7 was 7 books.

This is confusing.

Perhaps the worksheet uses “IIII” to represent 5, even without the slash, because in handwriting, the slash is often omitted in print.

Let me check online or recall: in many elementary worksheets, they write "IIII" for 5, implying the fifth mark is crossed, but in text it's not shown.

Moreover, for 6: “IIII III” — if “IIII” = 5, then 5 + 3 = 8.

For 7: “IIII II” = 5 + 2 = 7.

For 5½: “IIII” = 5.

For 5¾: “IIII” = 5.

For 6½: “IIII” = 5.

That seems consistent.

And for 5¼: “I” = 1

5: “II” = 2

6¼: “II” = 2

6¾: “II” = 2

7¼: “I” = 1

Let’s go with that, as it’s standard in such problems.

So filling frequencies:

Left table:

- 5: 2
- 5¼: 1
- 5½: 5 (since "IIII" = 5)
- 5¾: 5 ("IIII" = 5)
- 6: 8 ("IIII III" = 5 + 3)

Right table:

- 6¼: 2 ("II")
- 6½: 5 ("IIII" = 5)
- 6¾: 2 ("II")
- 7: 7 ("IIII II" = 5 + 2)
- 7¼: 1 ("I")

Now, let’s verify total number of books.

Add all frequencies:

Left: 2 + 1 + 5 + 5 + 8 = 21

Right: 2 + 5 + 2 + 7 + 1 = 17

Total = 21 + 17 = 38 books.

Now answer questions.

Question 3: What was the most common book height?

Look at frequencies:

- 5: 2
- 5¼: 1
- 5½: 5
- 5¾: 5
- 6: 8 ← highest so far
- 6¼: 2
- 6½: 5
- 6¾: 2
- 7: 7
- 7¼: 1

So 6 inches has 8 books — highest frequency.

Answer: 6 inches

Question 4: How much taller than the shortest book was the tallest book?

Shortest height: 5 inches

Tallest height: 7¼ inches

Difference: 7¼ - 5 = 2¼ inches

Answer: 2¼ inches

Question 5: How many more books are 7 inches tall than 6¾ inches tall?

7 inches: 7 books

6¾ inches: 2 books

Difference: 7 - 2 = 5

Answer: 5

Question 6: How many books are there in total on the bookshelf?

As calculated: 38

Answer: 38

Question 7: True or false

a) Most of the books are more than 6 inches tall.

“Most” means more than half.

Total books: 38

Half is 19.

Books more than 6 inches tall: that means >6, so 6¼, 6½, 6¾, 7, 7¼

Frequencies:

6¼: 2

6½: 5

6¾: 2

7: 7

7¼: 1

Sum: 2+5+2+7+1 = 17

17 < 19, so not most.

Also, books exactly 6 inches are not included in “more than 6”.

So 17 out of 38 is less than half.

Thus, false.

b) A third of the books are less than 6 inches tall.

Less than 6 inches: 5, 5¼, 5½, 5¾

Frequencies:

5: 2

5¼: 1

5½: 5

5¾: 5

Sum: 2+1+5+5 = 13