Population of Towns The data show the population (in thousands) of several towns. 14.6 19.3 10.6 18.9 5.8 6 58.6 26 2.5 30 55.5 5.5 18.3 26.6

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**NOTE** please see attached picture of graph

 

Population of Towns The data show the population (in thousands) of several towns.

14.6
19.3
10.6
18.9
5.8
6
58.6
26
2.5
30
55.5
5.5
18.3
26.6
 
 
 
### Understanding Boxplots: An Educational Guide

Boxplots, also known as box-and-whisker plots, are a standardized way of displaying the distribution of data based on a five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

#### Boxplot Interpretation

The boxplot shown in the image represents the population of towns (in thousands) and provides insights into the data distribution.

##### Explanation of the Boxplot Diagram

- **Horizontal Axis (X-axis):** The X-axis indicates the population of towns measured in thousands. The scale ranges from 0 to 60.
- **Vertical Box:** The vertical box represents the interquartile range (IQR) which contains the middle 50% of the data. 
    - The left (lower) edge of the box aligns with the first quartile (Q1), which is the 25th percentile of the data.
    - The right (upper) edge of the box aligns with the third quartile (Q3), which is the 75th percentile of the data.
    - The bold line inside the box represents the median (Q2), also known as the 50th percentile of the data. 
- **Whiskers:** The lines that extend from either side of the box (left and right) represent the range of the data excluding outliers.
    - The left whisker extends from the minimum value to the first quartile (Q1).
    - The right whisker extends from the third quartile (Q3) to the maximum value.

##### Additional Details

- **Outliers:** Any data points that lie outside 1.5 times the interquartile range from the quartiles are considered outliers and are often marked with individual points.
- **Data Distribution:**
    - The minimum value corresponds to approximately 15.
    - The first quartile (Q1) is around 20.
    - The median (Q2) is at 25.
    - The third quartile (Q3) is close to 30.
    - The maximum value is around 35.

This boxplot helps in understanding the central tendency and spread of the population data of the towns. It also assists in identifying any potential outliers or unusual observations within the data set.
Transcribed Image Text:### Understanding Boxplots: An Educational Guide Boxplots, also known as box-and-whisker plots, are a standardized way of displaying the distribution of data based on a five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. #### Boxplot Interpretation The boxplot shown in the image represents the population of towns (in thousands) and provides insights into the data distribution. ##### Explanation of the Boxplot Diagram - **Horizontal Axis (X-axis):** The X-axis indicates the population of towns measured in thousands. The scale ranges from 0 to 60. - **Vertical Box:** The vertical box represents the interquartile range (IQR) which contains the middle 50% of the data. - The left (lower) edge of the box aligns with the first quartile (Q1), which is the 25th percentile of the data. - The right (upper) edge of the box aligns with the third quartile (Q3), which is the 75th percentile of the data. - The bold line inside the box represents the median (Q2), also known as the 50th percentile of the data. - **Whiskers:** The lines that extend from either side of the box (left and right) represent the range of the data excluding outliers. - The left whisker extends from the minimum value to the first quartile (Q1). - The right whisker extends from the third quartile (Q3) to the maximum value. ##### Additional Details - **Outliers:** Any data points that lie outside 1.5 times the interquartile range from the quartiles are considered outliers and are often marked with individual points. - **Data Distribution:** - The minimum value corresponds to approximately 15. - The first quartile (Q1) is around 20. - The median (Q2) is at 25. - The third quartile (Q3) is close to 30. - The maximum value is around 35. This boxplot helps in understanding the central tendency and spread of the population data of the towns. It also assists in identifying any potential outliers or unusual observations within the data set.
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