The boxplot shown below results from the heights (cm) of males listed in a data set. What do the numbers in that boxplot tell us? 154 172.5 195 188.7 182.7 The minimum height is cm, the first quartile Q, is (Type integers or decimals. Do not round.) cm, the second quartile Q2 (or the median) is cm, the third quartile Q is cm, and the maximum height isO cm.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
**Boxplot Interpretation of Male Heights**

The diagram shown is a boxplot, representing the distribution of heights (in centimeters) of males listed in a data set. A boxplot is a standardized way of displaying the distribution of data based on a five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

### Explanation of the Boxplot

1. **Minimum Height (Left Whisker)**: This represents the smallest data point within the dataset, which is 154 cm.
2. **First Quartile (Q1)**: This marks the 25th percentile of the data. 25% of the data points fall below this value, which is 168.7 cm.
3. **Median (Q2)**: The median is the midpoint of the dataset, where 50% of the data points fall below and 50% are above. This value is 172.5 cm.
4. **Third Quartile (Q3)**: This marks the 75th percentile of the data. 75% of the data points fall below this value, which is 182.7 cm.
5. **Maximum Height (Right Whisker)**: This represents the largest data point within the dataset, which is 195 cm.

### Structure of the Boxplot

- **Whiskers**: The two lines extending from the minimum to Q1 and from Q3 to the maximum, represent the range of the data.
- **Box**: The box itself captures the interquartile range (IQR), which is the range between Q1 (168.7 cm) and Q3 (182.7 cm).
- **Median Line**: Inside the box, there is a line indicating the median value (172.5 cm).

### Boxplot Summary

Below the boxplot diagram, there is a series of text boxes that directly correlate to these five key summary statistics:

1. The minimum height is **154** cm.
2. The first quartile \(Q_1\) is **168.7** cm.
3. The second quartile \(Q_2\) (or the median) is **172.5** cm.
4. The third quartile \(Q_3\) is **182.7** cm.
5. The maximum height is **195** cm.

Each of these values helps to understand the spread and central tendency of the
Transcribed Image Text:**Boxplot Interpretation of Male Heights** The diagram shown is a boxplot, representing the distribution of heights (in centimeters) of males listed in a data set. A boxplot is a standardized way of displaying the distribution of data based on a five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. ### Explanation of the Boxplot 1. **Minimum Height (Left Whisker)**: This represents the smallest data point within the dataset, which is 154 cm. 2. **First Quartile (Q1)**: This marks the 25th percentile of the data. 25% of the data points fall below this value, which is 168.7 cm. 3. **Median (Q2)**: The median is the midpoint of the dataset, where 50% of the data points fall below and 50% are above. This value is 172.5 cm. 4. **Third Quartile (Q3)**: This marks the 75th percentile of the data. 75% of the data points fall below this value, which is 182.7 cm. 5. **Maximum Height (Right Whisker)**: This represents the largest data point within the dataset, which is 195 cm. ### Structure of the Boxplot - **Whiskers**: The two lines extending from the minimum to Q1 and from Q3 to the maximum, represent the range of the data. - **Box**: The box itself captures the interquartile range (IQR), which is the range between Q1 (168.7 cm) and Q3 (182.7 cm). - **Median Line**: Inside the box, there is a line indicating the median value (172.5 cm). ### Boxplot Summary Below the boxplot diagram, there is a series of text boxes that directly correlate to these five key summary statistics: 1. The minimum height is **154** cm. 2. The first quartile \(Q_1\) is **168.7** cm. 3. The second quartile \(Q_2\) (or the median) is **172.5** cm. 4. The third quartile \(Q_3\) is **182.7** cm. 5. The maximum height is **195** cm. Each of these values helps to understand the spread and central tendency of the
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman