Box and Whisker Plots Notes and Worksheets - Lindsay Bowden - Free Printable

Here are the step-by-step solutions for each problem on the worksheet.

Problem 1

Question: Would range or IQR be more appropriate in this data set: 32, 35, 76, 29, 30, 32, 31, 39, 28, 34?

* Step 1: Look at the numbers. Most of them are between 28 and 39.
* Step 2: Notice the number 76. It is much larger than all the other numbers. This is called an outlier.
* Step 3: The Range uses the minimum and maximum values. Because 76 is so big, it makes the Range very large and doesn't represent the "typical" spread of the data well.
* Step 4: The IQR (Interquartile Range) looks at the middle 50% of the data. It ignores the outliers like 76. Therefore, it gives a better description of the main group of numbers.

Answer: IQR

---

Problem 2

Question: Find the max, min, Q1, Q2, and Q3 of the data set: 8, 2, 10, 9, 7, 5, 13, 4, 8, 12, 16.

* Step 1: Order the data from least to greatest:
2, 4, 5, 7, 8, 8, 9, 10, 12, 13, 16
* Step 2: Find the Min (smallest) and Max (largest).
* Min: 2
* Max: 16
* Step 3: Find Q2 (the Median). There are 11 numbers. The middle number is the 6th one.
* Q2: 8
* Step 4: Find Q1 (Median of the lower half). The lower half is: 2, 4, 5, 7, 8. The middle number is 5.
* Q1: 5
* Step 5: Find Q3 (Median of the upper half). The upper half is: 9, 10, 12, 13, 16. The middle number is 12.
* Q3: 12

Answer:
* Max: 16
* Min: 2
* Q1: 5
* Q2: 8
* Q3: 12

---

Problem 3

Question: Label the Q1, Q2, Q3 on the box and whisker plot. Then, find the range and IQR.
*(Looking at the plot provided in #3)*

* Step 1: Identify the parts of the plot based on the number line.
* Left whisker end (Min): 5
* Left side of box (Q1): 10
* Line inside box (Q2/Median): 15
* Right side of box (Q3): 30
* Right whisker end (Max): 45
* Step 2: Calculate the Range.
* Formula: Max - Min
* Calculation: $45 - 5 = 40$
* Step 3: Calculate the IQR.
* Formula: Q3 - Q1
* Calculation: $30 - 10 = 20$

Answer:
* Q1: 10
* Q2: 15
* Q3: 30
* Range: 40
* IQR: 20

---

Problem 4

Question: Draw a box and whisker plot using the following data: 62, 73, 65, 70, 72, 95, 109, 106, 99, 73, 85, 89, 91.

* Step 1: Order the data from least to greatest:
62, 65, 70, 72, 73, 73, 85, 89, 91, 95, 99, 106, 109
* Step 2: Find the Five-Number Summary.
* Min: 62
* Q1: The median of the lower half (62, 65, 70, 72, 73, 73) is the average of 70 and 72 $\rightarrow$ 71
* Q2 (Median): The middle number of the whole set is 73
* Q3: The median of the upper half (85, 89, 91, 95, 99, 106, 109) is 95
* Max: 109
* Step 3: Drawing instructions.
* Draw a vertical line at 62 and 109 (whiskers).
* Draw a box starting at 71 and ending at 95.
* Draw a vertical line inside the box at 73.

Answer:
* Min: 62
* Q1: 71
* Median: 73
* Q3: 95
* Max: 109
*(Draw the plot using these points)*

---

Problems 5–10

*(Based on the temperature box plot at the bottom)*
*Plot Values:* Min=35, Q1=37, Median=40, Q3=42, Max=43.

5. What was the lowest temperature recorded?
* Look at the end of the left whisker.
* Answer: 35°

6. What percentage of the temperatures were above 37°?
* 37° is Q1 (the first quartile).
* Q1 marks the bottom 25% of the data. Everything above it is the remaining 75%.
* Answer: 75%

7. What percentage of the temperatures were above 40°?
* 40° is the Median (Q2).
* The median splits the data exactly in half.
* Answer: 50%

8. What is the Q1 and Q3 for this data set?
* Read the edges of the box on the number line.
* Left edge (Q1) is 37. Right edge (Q3) is 42.
* Answer: Q1: 37, Q3: 42

9. What percentage of the temperatures were below 37°?
* 37° is Q1. By definition, 25% of the data falls below Q1.
* Answer: 25%

10. What was the median temperature in January?
* Look for the vertical line inside the box.
* Answer: 40°