Box and whisker questions focus on understanding data distribution through visual representation. This resource provides practice problems and explanations on how to create and interpret box-and-whisker plots. Ideal for students learning statistics, the material covers key concepts such as quartiles, medians, and extremes. Engage with various datasets to enhance your analytical skills and grasp the significance of data visualization in statistics.

Key Points

  • Explains how to create box-and-whisker plots using given datasets.
  • Includes practice questions to reinforce understanding of quartiles and medians.
  • Covers interpretation of data distribution and identification of outliers.
  • Provides step-by-step guidance for analyzing statistical data visually.
newtopiccyclegrowin
11 pages
Language:English
Type:Study Guide
Biology
newtopiccyclegrowin
11 pages
Language:English
Type:Study Guide
Biology
375
/ 11
NAME_________
Name Date
Copyright © Houghton Mifflin Company. All rights reserved.
Use with text pages 246–247.
Reteach
1 0.5
Make a Box-and-Whisker Plot
Use the following data to make a box-and-whisker plot.
14, 21, 19, 12, 13, 24, 26, 19, 15, 25, 19
Name Date
Step 1: Order the data from least to greatest.
Step 2: Circle the median. Then find the upper and lower quartiles. Imagine breaking
the data set into two parts at the median. The quartiles are the medians of the two parts.
Step 3: Circle the extremes — the greatest and least values of the data set.
Step 4: Draw a number line that includes all of the numbers in the data set. Above the line,
draw points for the median, quartiles, and extremes.
Step 5: Draw a box that begins at the lower quartile and ends at the upper quartile.
Draw a line through the box at the median.
Step 6: Draw whiskers from both ends of the box. The whiskers end at the extremes.
12
13 14 15 16
17 18 19 20 21 22 23 24 25 26
lower
extreme
upper
extreme
upper
quartile
lower
quartile
median
• ••••
Use the data set below for Problems 1–6.
58, 71, 51, 67, 58, 55, 53, 57, 58, 62, 65
1. What is the median of the data set?
2. What are the upper and lower quartiles?
3. What are the extremes of the data set?
4. Draw a box-and-whisker plot to display the data.
5. How much of the data are in the box?
6. How much of the data are in the whiskers?
Name Date
Copyright © Houghton Mifflin Company. All rights reserved.
Use with text pages 248–249.
Reteach
1 0.6
Box-and-Whisker Plots
Maria recorded the number of days it rained or
snowed each month during the past year. This
box-and-whisker plot displays her data.
The extremes tell you
• the least number of days it rained or snowed in a month was 2.
• the greatest number of days it rained or snowed in a month was 10.
The median tells you
•
ᎏ
1
2
ᎏ
of the months had over 6 days of rain or snow.
•
ᎏ
1
2
ᎏ
of the months had fewer than 6 days of rain or snow.
The data clusters tell you
•
ᎏ
1
4
ᎏ
of the data clusters between 2 and 3 days.
•
ᎏ
1
4
ᎏ
of the data clusters between 6 and 7 days.
Use the box-and-whisker plot below for Problems 1–5.
1. What are the least and greatest number of baskets made?
2. What is the median number of baskets made?
3. What are the upper and lower quartiles for the data?
4. Where are the data clustered?
5. What do the extremes tell you about the number of baskets made?
12345678910
Days of Rain or Snow
Baskets Made
5
10 15
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End of Document
375

Figures

box-and-whisker plot
For Exercises 1–6, refer to the table at the right. It
For Exercises 1–6, use the table below. It shows the number of

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FAQs

What is the purpose of a box-and-whisker plot?
A box-and-whisker plot is a diagram that divides data into four equal parts, allowing for the visualization of the distribution of a data set. It helps identify the median, lower quartile, upper quartile, and extremes of the data. This type of plot is particularly useful for understanding the spread and clustering of the data, making it easier to identify outliers and the overall range.
How do you determine the quartiles in a box-and-whisker plot?
To determine the quartiles in a box-and-whisker plot, first, you need to order the data from least to greatest. The median of the data set is found, which divides the data into two halves. The lower quartile (LQ) is the median of the lower half, while the upper quartile (UQ) is the median of the upper half. This process helps in accurately representing the distribution of the data.
What steps are involved in creating a box-and-whisker plot?
Creating a box-and-whisker plot involves several steps. First, order the data from least to greatest and find the median. Next, identify the lower and upper quartiles by finding the medians of the lower and upper halves of the data set. Then, draw a number line that includes the range of the data, plotting points for the median, quartiles, and extremes. Finally, draw a box from the lower to upper quartile and extend whiskers to the extremes.
What does the interquartile range represent?
The interquartile range (IQR) represents the range between the lower quartile and the upper quartile in a box-and-whisker plot. It measures the spread of the middle 50% of the data, providing insights into the variability and concentration of the data points. A larger IQR indicates greater variability, while a smaller IQR suggests that the data points are more closely clustered around the median.
How can outliers be identified using a box-and-whisker plot?
Outliers can be identified in a box-and-whisker plot by examining the whiskers and the data points that fall outside of them. Typically, any data point that lies beyond 1.5 times the interquartile range above the upper quartile or below the lower quartile is considered an outlier. This method helps in recognizing values that significantly differ from the rest of the data set.
What information can be derived from the extremes in a box-and-whisker plot?
The extremes in a box-and-whisker plot provide valuable information about the minimum and maximum values of the data set. The lower extreme indicates the smallest value, while the upper extreme indicates the largest value. This information helps to understand the overall range of the data and can highlight potential outliers or unusual data points that fall outside the expected range.

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