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-by-step:
1. Look at the numbers. Most of them are grouped together between 28 and 39.
2. However, there is one number, 76, that is much larger than the rest. This is called an outlier.
3. The Range uses the minimum and maximum values. Because 76 is so big, it would make the range huge and not tell us much about the typical numbers.
4. The IQR (Interquartile Range) looks at the middle 50% of the data. It ignores outliers like 76.
5. Therefore, IQR is better because it gives a more accurate picture of the main group of data.

Answer: IQR

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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-by-step:
1. Order the data from least to greatest:
2, 4, 5, 7, 8, 8, 9, 10, 12, 13, 16
2. Find Min and Max:
* Min (lowest): 2
* Max (highest): 16
3. Find Q2 (Median):
* There are 11 numbers. The median is the exact middle number (the 6th one).
* Counting to the 6th number: 2, 4, 5, 7, 8, 8.
* Q2 = 8
4. Find Q1 (Lower Quartile):
* Look at the lower half (numbers to the left of the median): 2, 4, 5, 7, 8.
* The median of this lower half is 5.
* Q1 = 5
5. Find Q3 (Upper Quartile):
* Look at the upper half (numbers to the right of the median): 9, 10, 12, 13, 16.
* The median of this upper half is 12.
* Q3 = 12

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

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Problem 3

Question: Label the Q1, Q2, Q3 on the box and whisker plot. Then, find the range and IQR.
*(Based on the visual plot provided: Left dot=5, Box Start=10, Line inside box=15, Box End=30, Right dot=45)*

Step-by-step:
1. Identify parts of the plot:
* 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
2. Calculate Range:
* Formula: Max - Min
* $45 - 5 = 40$
3. Calculate IQR:
* Formula: Q3 - Q1
* $30 - 10 = 20$

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

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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-by-step:
1. Order the data:
62, 65, 70, 72, 73, 73, 85, 89, 91, 95, 99, 106, 109
2. Find the Five Number Summary:
* Min: 62
* Max: 109
* Q2 (Median): There are 13 numbers. The middle is the 7th number.
Count: 62, 65, 70, 72, 73, 73, 85. So, Q2 = 85.
* Q1: Median of the lower half (62, 65, 70, 72, 73, 73).
Middle two are 70 and 72. Average: $(70+72)/2 = 71$. So, Q1 = 71.
* Q3: Median of the upper half (89, 91, 95, 99, 106, 109).
Middle two are 95 and 99. Average: $(95+99)/2 = 97$. So, Q3 = 97.
3. Drawing Instructions:
* Draw a dot at 62 and a line to a box starting at 71.
* Draw a vertical line inside the box at 85.
* End the box at 97 and draw a line to a dot at 109.

Answer:
* Min: 62
* Q1: 71
* Median: 85
* Q3: 97
* Max: 109

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Problems 5–10

*(Using the temperature box plot: Min=35, Q1=37, Median=40, Q3=42, Max=43)*

5. What was the lowest temperature recorded?
* The lowest point on the plot (the end of the left whisker) is at 35.
* Answer: 35°

6. What percentage of the temperatures were above 37°?
* 37° is Q1 (the first quartile).
* By definition, 25% of data is below Q1, and 75% is above Q1.
* Answer: 75%

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

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

9. What percentage of the temperatures were below 37°?
* 37° is Q1.
* The first quartile represents the bottom 25% of the data.
* Answer: 25%

10. What was the median temperature in January?
* The median is the line inside the box. It aligns with 40.
* Answer: 40°