Worksheet on histograms with three data sets to graph: children's ages, training hours, and basketball shots made.

Let’s solve each histogram problem step by step.

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Problem 1: Children’s Ages

Data given:
2, 3, 4, 4, 5, 7, 7, 6

We need to count how many children are in each age group (bin):

- Age 2 → appears 1 time
- Age 3 → appears 1 time
- Age 4 → appears 2 times
- Age 5 → appears 1 time
- Age 6 → appears 1 time
- Age 7 → appears 2 times

So the frequencies for ages 2 through 7 are:

Age | Frequency
2 | 1
3 | 1
4 | 2
5 | 1
6 | 1
7 | 2

Now draw bars on the histogram with these heights.

→ Bar at age 2: height = 1
→ Bar at age 3: height = 1
→ Bar at age 4: height = 2
→ Bar at age 5: height = 1
→ Bar at age 6: height = 1
→ Bar at age 7: height = 2

(No data for age 8 or higher — so no bar there.)

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Problem 2: Training Runs (miles)

Data:
11, 13, 9, 14, 3, 12, 10, 7, 9, 8, 10

First, sort them to make counting easier:
3, 7, 8, 9, 9, 10, 10, 11, 12, 13, 14

The x-axis is labeled “Number of Miles” from 0 to 14, in bins of 2? Wait — looking at the axis labels: 0, 2, 4, 6, 8, 10, 12, 14 — so likely each bin covers a range of 2 miles.

But let’s check the example in the top right: Gas Scores used bins like 10–14, 15–19, etc. So probably here, since the axis goes 0,2,4,...,14, each bar represents a 2-mile interval.

Common way: Bin ranges might be:

- 0–1.999… → but since we have whole numbers, better to think:

Actually, looking at the data and typical school histograms, they often use intervals like:

Bin 0–2: includes 0,1,2
Bin 2–4: includes 2,3,4? But that would overlap.

Wait — standard practice: if axis says 0,2,4,6..., then bins are usually:

[0,2), [2,4), [4,6), [6,8), [8,10), [10,12), [12,14)

But since our data has integers, let’s assign:

- 0 ≤ x < 2 → only 0,1 → none in data
- 2 ≤ x < 4 → 2,3 → we have 3
- 4 ≤ x < 6 → 4,5 → none
- 6 ≤ x < 8 → 6,7 → we have 7
- 8 ≤ x < 10 → 8,9 → we have 8,9,9 → that’s 3 values
- 10 ≤ x < 12 → 10,11 → we have 10,10,11 → 3 values
- 12 ≤ x < 14 → 12,13 → we have 12,13 → 2 values
- 14 ≤ x < 16 → 14 → we have 14 → 1 value

Wait — but the axis only goes to 14, and last label is 14. Maybe the last bin is 14–16? Or perhaps inclusive?

Looking back at the example: Gas Scores had bins 10–14, 15–19, 20–24, 25–29, 30–34 — so each bin is 5 units wide, starting at 10.

In Problem 2, the x-axis labels are 0,2,4,6,8,10,12,14 — so likely each bin is 2 units wide, and centered or starting at those points.

Another common approach: the tick marks are the *start* of each bin.

So:

Bin starting at 0: 0–1.999 → includes 0,1 → no data
Bin starting at 2: 2–3.999 → includes 2,3 → we have 3 → count=1
Bin starting at 4: 4–5.999 → 4,5 → none
Bin starting at 6: 6–7.999 → 6,7 → we have 7 → count=1
Bin starting at 8: 8–9.999 → 8,9 → we have 8,9,9 → count=3
Bin starting at 10: 10–11.999 → 10,11 → we have 10,10,11 → count=3
Bin starting at 12: 12–13.999 → 12,13 → we have 12,13 → count=2
Bin starting at 14: 14–15.999 → 14 → we have 14 → count=1

Yes, this makes sense.

So frequency per bin:

Start at 0: 0
Start at 2: 1 (value: 3)
Start at 4: 0
Start at 6: 1 (value: 7)
Start at 8: 3 (values: 8,9,9)
Start at 10: 3 (values: 10,10,11)
Start at 12: 2 (values: 12,13)
Start at 14: 1 (value: 14)

So draw bars accordingly.

Note: The y-axis is “Number of Runs”, so height = frequency.

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Problem 3: Shots Made

Data:
11, 22, 8, 16, 14, 14, 7, 17, 9, 15, 10, 22, 21

Sort them:
7, 8, 9, 10, 11, 14, 14, 15, 16, 17, 21, 22, 22

X-axis: Number of Shots Made, labeled 0,4,8,12,16,20,24 — so bins of width 4.

Likely bins:

0–3.999 → 0,1,2,3 → none
4–7.999 → 4,5,6,7 → we have 7 → count=1
8–11.999 → 8,9,10,11 → we have 8,9,10,11 → count=4
12–15.999 → 12,13,14,15 → we have 14,14,15 → count=3
16–19.999 → 16,17,18,19 → we have 16,17 → count=2
20–23.999 → 20,21,22,23 → we have 21,22,22 → count=3
24–27.999 → 24+ → none

Check total: 1 + 4 + 3 + 2 + 3 = 13 → matches number of players.

So:

Bin 0–4: 0
Bin 4–8: 1 (shot=7)
Bin 8–12: 4 (shots=8,9,10,11)
Bin 12–16: 3 (shots=14,14,15)
Bin 16–20: 2 (shots=16,17)
Bin 20–24: 3 (shots=21,22,22)
Bin 24–28: 0

Draw bars with these heights.

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Final Answer:

For each histogram, fill in the bars as follows:

Problem 1 (Children’s Ages):
Bar heights for ages 2 to 7:
Age 2: 1
Age 3: 1
Age 4: 2
Age 5: 1
Age 6: 1
Age 7: 2

Problem 2 (Training Runs):
Bar heights for bins starting at:
0: 0
2: 1
4: 0
6: 1
8: 3
10: 3
12: 2
14: 1

Problem 3 (Shots Made):
Bar heights for bins:
0–4: 0
4–8: 1
8–12: 4
12–16: 3
16–20: 2
20–24: 3
24–28: 0

*(Note: Since you’re drawing on paper, just make sure each bar’s height matches the frequency counted above.)*