Graph Worksheets | Learning to Work with Charts and Graphs - Free Printable

Sure! Let’s solve each problem step by step. The goal is to find the five-number summary for each data set, which consists of:

- Minimum: smallest value
- Q₁ (First Quartile): median of the lower half (not including overall median if odd number of data points)
- Q₂ (Median): middle value when data is ordered
- Q₃ (Third Quartile): median of the upper half
- Maximum: largest value

Then we’ll describe how to draw the box-and-whisker plot on the given number line.

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## 🔢 Problem 1:
Data Set: 7, 25, 18, 1, 24, 3, 11, 9, 15, 22, 23, 5, 12
→ Step 1: Sort the data in ascending order

Sorted:
1, 3, 5, 7, 9, 11, 12, 15, 18, 22, 23, 24, 25

→ Step 2: Count the data points
There are 13 values → odd number → median is the 7th value.

→ Step 3: Find five-number summary

- Minimum = 1
- Maximum = 25
- Q₂ (Median) = 7th value = 12
- Lower Half (first 6 values): 1, 3, 5, 7, 9, 11 → Q₁ = median of these = average of 3rd and 4th = (5 + 7)/2 = 6
- Upper Half (last 6 values): 15, 18, 22, 23, 24, 25 → Q₃ = median of these = average of 3rd and 4th = (22 + 23)/2 = 22.5

✔ Five-number summary for #1:
Min = 1, Q₁ = 6, Q₂ = 12, Q₃ = 22.5, Max = 25

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## 📊 How to draw Box-and-Whisker Plot for #1:

On the number line from 1 to 25:

- Draw a whisker from 1 (min) to 6 (Q₁)
- Draw a box from 6 (Q₁) to 22.5 (Q₃)
- Inside the box, mark a line at 12 (median)
- Draw a whisker from 22.5 (Q₃) to 25 (max)

*(Note: Since Q₃ = 22.5, you’ll need to place it halfway between 22 and 23 on the number line.)*

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## 🔢 Problem 2:
Data Set: 1, 24, 13, 4, 11, 7, 22, 15, 19
→ Step 1: Sort the data

Sorted:
1, 4, 7, 11, 13, 15, 19, 22, 24

→ Step 2: Count → 9 values → odd → median is 5th value

→ Step 3: Five-number summary

- Minimum = 1
- Maximum = 24
- Q₂ (Median) = 5th value = 13
- Lower Half (first 4 values): 1, 4, 7, 11 → Q₁ = median = (4 + 7)/2 = 5.5
- Upper Half (last 4 values): 15, 19, 22, 24 → Q₃ = median = (19 + 22)/2 = 20.5

✔ Five-number summary for #2:
Min = 1, Q₁ = 5.5, Q₂ = 13, Q₃ = 20.5, Max = 24

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## 📊 How to draw Box-and-Whisker Plot for #2:

- Whisker from 1 to 5.5
- Box from 5.5 to 20.5
- Median line at 13
- Whisker from 20.5 to 24

*(Place Q₁ at halfway between 5 and 6; Q₃ at halfway between 20 and 21.)*

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## 🔢 Problem 3:
Data Set: 6, 9, 7, 13, 10, 12, 8, 15, 19, 2, 11
→ Step 1: Sort the data

Sorted:
2, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19

→ Step 2: Count → 11 values → odd → median is 6th value

→ Step 3: Five-number summary

- Minimum = 2
- Maximum = 19
- Q₂ (Median) = 6th value = 10
- Lower Half (first 5 values): 2, 6, 7, 8, 9 → Q₁ = median = 7
- Upper Half (last 5 values): 11, 12, 13, 15, 19 → Q₃ = median = 13

✔ Five-number summary for #3:
Min = 2, Q₁ = 7, Q₂ = 10, Q₃ = 13, Max = 19

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## 📊 How to draw Box-and-Whisker Plot for #3:

- Whisker from 2 to 7
- Box from 7 to 13
- Median line at 10
- Whisker from 13 to 19

*(All values are whole numbers — easy to plot exactly on the number line.)*

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## ✔ Final Answers to Fill In:

1)

Minimum: 1
Maximum: 25
Q₁: 6
Q₂: 12
Q₃: 22.5

2)

Minimum: 1
Maximum: 24
Q₁: 5.5
Q₂: 13
Q₃: 20.5

3)

Minimum: 2
Maximum: 19
Q₁: 7
Q₂: 10
Q₃: 13

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📌 Tip for drawing plots: Use a ruler if possible. Mark the 5 key points first (min, Q₁, Q₂, Q₃, max), then draw the box and whiskers accordingly.

Let me know if you’d like me to sketch the actual plots visually — though since this is text-based, I’ve described them precisely so you can draw them accurately!

Good luck! 😊