Grade 6 Box Plots Worksheets 2024 - Free Printable

The image you've uploaded is an answer key for a worksheet on box-and-whisker plots (also known as box plots). It provides the correct values and visual representations for three different data sets. Let's go through each problem step-by-step to explain how the answers were derived, so you understand the process of creating a box-and-whisker plot.

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🔷 What is a Box-and-Whisker Plot?

A box-and-whisker plot displays the five-number summary of a data set:
1. Minimum – smallest value
2. Q₁ (First Quartile) – median of the lower half
3. Q₂ (Median) – middle value of the entire data set
4. Q₃ (Third Quartile) – median of the upper half
5. Maximum – largest value

These five numbers are used to draw the plot:
- A box from Q₁ to Q₃
- A line inside the box at Q₂ (median)
- Whiskers extending from the box to the minimum and maximum values

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## ✔ Problem 1:
Data: 17, 29, 32, 9, 30, 14, 8, 39, 11, 32, 23

Step 1: Sort the data

Arrange in ascending order:
8, 9, 11, 14, 17, 23, 29, 30, 32, 32, 39

Step 2: Find the five-number summary

- Minimum: 8 ✔
- Maximum: 39 ✔

- Median (Q₂): The middle value. There are 11 values → the 6th value is 23 ✔
- Q₁ (First Quartile): Median of the lower half (first 5 values):
Lower half: 8, 9, 11, 14, 17 → median = 11 ✔
- Q₃ (Third Quartile): Median of the upper half (last 5 values):
Upper half: 29, 30, 32, 32, 39 → median = 32 ✔

✔ So:
- Min = 8
- Max = 39
- Q₁ = 11
- Q₂ = 23
- Q₃ = 32

This matches the answer key.

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## ✔ Problem 2:
Data: 58, 67, 44, 72, 51, 42, 60, 46, 69

Step 1: Sort the data

42, 44, 46, 51, 58, 60, 67, 69, 72

(9 values)

Step 2: Five-number summary

- Min: 42 ✔
- Max: 72 ✔
- Median (Q₂): Middle value (5th) = 58 ✔
- Q₁: Lower half: 42, 44, 46, 51 → median of 4 values = average of 2nd and 3rd = (44 + 46)/2 = 45 ✔
- Q₃: Upper half: 60, 67, 69, 72 → median = (67 + 69)/2 = 68 ✔

✔ All values match the answer key.

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## ✔ Problem 3:
Data: 67, 100, 94, 77, 80, 62, 79, 68, 95, 86, 73, 84

Step 1: Sort the data

62, 67, 68, 73, 77, 79, 80, 84, 86, 94, 95, 100

(12 values)

Step 2: Five-number summary

- Min: 62 ✔
- Max: 100 ✔

- Median (Q₂): Average of 6th and 7th values:
79 and 80 → (79 + 80)/2 = 79.5 ✔

- Q₁: First half: 62, 67, 68, 73, 77, 79 → median of 6 values = average of 3rd and 4th = (68 + 73)/2 = 70.5 ✔

- Q₃: Second half: 80, 84, 86, 94, 95, 100 → median = (86 + 94)/2 = 90 ✔

✔ Matches the answer key.

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📊 Summary of Key Concepts:

| Term | Meaning |
|------|--------|
| Minimum | Smallest number in the data set |
| Maximum | Largest number in the data set |
| Q₁ | Median of the lower half (first 50%) |
| Q₂ (Median) | Middle value of the entire data set |
| Q₃ | Median of the upper half (last 50%) |

When there’s an even number of data points, the median is the average of the two middle numbers. For quartiles, split the data into halves and find the median of each half.

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✔ Final Answer Check:

All values in the answer key are correct based on standard box-and-whisker plot procedures.

Let me know if you'd like help drawing these plots or interpreting them!