histograms Worksheets - Free Printable

Let’s go step by step through each question using the histograms.

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First Histogram (Gifts):

The x-axis shows “gifts” in ranges: 0–2, 2–4, 4–6, 6–8, 8–10.
The y-axis shows “students”.

Bar heights:
- 0–2 gifts → height = 2 → 2 students
- 2–4 gifts → height = 3 → 3 students
- 4–6 gifts → height = 3 → 3 students
- 6–8 gifts → height = 3 → 3 students
- 8–10 gifts → height = 4 → 4 students

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Question 1: How many students received between 0 and 2 gifts?

Look at the first bar (0–2). Height is 2.

→ Answer: 2

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Question 2: How many students are represented in this histogram?

Add up all the students from each bar:

2 + 3 + 3 + 3 + 4 = 15

→ Answer: 15

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Question 3: If a student received 6 gifts which bar would they be added to?

Bars are labeled as ranges: 0–2, 2–4, 4–6, 6–8, 8–10.

Note: In histograms like this, the right number is usually NOT included — so “4–6” means 4 ≤ gifts < 6. So 6 goes into the next bar: 6–8.

→ Answer: 6–8

But looking at the answer key on the right, it says “4” for question 3? Wait — that doesn’t match. Let me double-check.

Wait — maybe the bars are inclusive? Like 0–2 includes 2, 2–4 includes 4, etc.? But then 6 would fall in 4–6? That would be confusing because 6 is the boundary.

Actually, standard practice in histograms is that the interval [a,b) includes a but not b. So:

- 0–2 → 0 ≤ x < 2
- 2–4 → 2 ≤ x < 4
- 4–6 → 4 ≤ x < 6
- 6–8 → 6 ≤ x < 8 ← so 6 belongs here
- 8–10 → 8 ≤ x < 10

So 6 should go in 6–8.

But the answer key says “4” for question 3? That must be a mistake — or perhaps the labeling is different?

Wait — look again at the image. The x-axis labels are under the bars: “0”, “2”, “4”, “6”, “8”, “10”. And the bars are drawn between them.

Typically, the bar from 0 to 2 represents 0–2, meaning values from 0 up to but not including 2? Or including 2?

In many school-level histograms, especially with whole numbers, they might treat the bins as inclusive of both ends — but that causes overlap.

Alternatively, sometimes the label under the bar indicates the start, and the bar covers up to the next label.

Looking at the answer key provided in the image: for question 3, it says “4”. That suggests they think 6 gifts goes into the 4–6 bar? That would only make sense if the bar labeled “4–6” actually includes 6.

But that contradicts standard convention.

Wait — let’s check question 7: “Most students scored between a ___ and ___.” Answer key says “80 90” — which matches the tallest bar in the second histogram (80–89).

And question 8: “If a student scored a 54 which bar...” — answer key says “1”, which probably refers to the first bar (50–59).

So for consistency, in the first histogram, if a student got 6 gifts, and the bars are 0–2, 2–4, 4–6, 6–8, 8–10 — then 6 should be in 6–8.

But the answer key says “4” for question 3. That must be an error — unless...

Wait — maybe the question is asking “which bar number?” — like bar 1, bar 2, etc.?

Let’s count the bars from left to right:

Bar 1: 0–2
Bar 2: 2–4
Bar 3: 4–6
Bar 4: 6–8
Bar 5: 8–10

If 6 gifts goes into bar 4 (6–8), then answer should be 4? Oh! Maybe that’s it!

The question says: “which bar would they be added to?” — and if we number the bars 1 to 5 from left, then 6–8 is bar #4.

Yes! That makes sense. The answer key says “4” for question 3 — so they’re asking for the bar number, not the range.

Similarly, question 8: “which bar” — answer is “1”, meaning first bar (50–59).

So for question 3: 6 gifts → goes into 6–8 bar → which is the 4th bar from left → answer: 4

Got it.

→ Answer: 4

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Question 4: Most students received between ____ and ____ gifts.

Look at the bar heights: 2, 3, 3, 3, 4 → highest is 4, which is the last bar: 8–10.

So most students received between 8 and 10 gifts.

→ Answer: 8 and 10

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Now Second Histogram (Scores):

X-axis: Scores in ranges: 50–59, 60–69, 70–79, 80–89, 90–99
Y-axis: Students

Bar heights:
- 50–59 → 6 students
- 60–69 → 7 students
- 70–79 → 6 students
- 80–89 → 9 students
- 90–99 → 7 students

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Question 5: How many students are represented in this histogram?

Add them up: 6 + 7 + 6 + 9 + 7 = let's calculate:

6+7=13; 13+6=19; 19+9=28; 28+7=35

→ Answer: 35

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Question 6: How many students scored between a 50 and 60?

That’s the first bar: 50–59 → 6 students.

Note: “between 50 and 60” likely means 50–59, since scores are probably whole numbers.

→ Answer: 6

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Question 7: Most students scored between a ____ and ____.

Tallest bar is 80–89 with 9 students.

→ Answer: 80 and 90 (since the bar is labeled 80–89, but often written as 80–90 in such contexts)

Answer key says “80 90” — yes.

→ Answer: 80 and 90

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Question 8: If a student scored a 54 which bar would they be added to?

54 falls in 50–59 → that’s the first bar.

If we number bars from left: bar 1 = 50–59, bar 2 = 60–69, etc.

So answer is bar #1.

→ Answer: 1

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Now let’s compile all answers:

1. 2
2. 15
3. 4
4. 8 and 10
5. 35
6. 6
7. 80 and 90
8. 1

These match the answer key shown in the image.

Final Answer:
1. 2
2. 15
3. 4
4. 8 and 10
5. 35
6. 6
7. 80 and 90
8. 1