​(a) Identify the shape of the​ distribution, and​ (b) determine the​ five-number summary. Assume that each number in the​ five-number summary is an integer.
0
10
20



A horizontal boxplot is above a number line from 0 to 20 in increments of 1 and consists of a box extending from 12 to 18 with a vertical line segment through the box at 17 and two horizontal line segments extending from the left and right sides of the box to 0 and 20, respectively.
Question content area bottom
Part 1
a. Choose the correct answer below for the shape of the distribution.
A.The distribution is skewed right.
The distribution is skewed right.
B.The distribution is roughly symmetric.
The distribution is roughly symmetric.
C.The distribution is skewed left.
The distribution is skewed left.
D.
The shape of the distribution cannot be determined from the boxplot.
Part 2
b. The​ five-number summary is 
  
enter your response here​, 
  
enter your response here​, 
  
enter your response here​, 
  
enter your response here​, 
  
enter your response here.


Let's break this problem down step-by-step.

### Part 1: Identify the Shape of the Distribution

We are given a boxplot with the following key information:
- The **box** extends from 12 to 18.
- The **median** (vertical line inside the box) is at 17.
- The **whiskers** extend from 0 (minimum) to 20 (maximum).

To determine the shape of the distribution:
- The **box** is not centered. It is closer to the higher end of the data range (from 12 to 18, but the median is at 17), meaning most of the data points are in the upper range.
- The **right whisker** is very short (from 18 to 20), while the **left whisker** is long (from 12 down to 0).

This suggests that there are fewer larger values and more smaller values, leading to a **left-skewed distribution** (skewed to the left). Thus, the correct answer is:

**(a)** C. The distribution is skewed left.

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### Part 2: Five-Number Summary

The five-number summary consists of:
1. **Minimum (Q₀)**: This is the smallest value. The whisker extends to 0, so the minimum is 0.
2. **First Quartile (Q₁)**: The lower end of the box. This is 12.
3. **Median (Q₂)**: The vertical line in the box. This is 17.
4. **Third Quartile (Q₃)**: The upper end of the box. This is 18.
5. **Maximum (Q₄)**: This is the largest value. The whisker extends to 20, so the maximum is 20.

So, the five-number summary is:
**(b)** 0, 12, 17, 18, 20.

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### Summary of Results:
- **(a)** The distribution is skewed left.
- **(b)** The five-number summary is: 0, 12, 17, 18, 20.

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Do you need more details or have any other questions?

Here are 5 related questions for practice:
1. How does the length of the whiskers in a boxplot affect the interpretation of skewness?
2. What would the boxplot look like if the distribution were symmetric?
3. How would the five-number summary change if the boxplot extended from 10 to 20?
4. What does the median tell you about the central tendency of the data?
5. How can outliers affect the whiskers in a boxplot?

**Tip:** Always check the length of the whiskers in a boxplot when determining skewness; a longer whisker on one side typically indicates the direction of skewness.

Identify the shape of the distribution and determine the five-number summary based on the given boxplot. The box extends from 12 to 18, with a median at 17, whiskers at 0 and 20.

Learn how to identify the skewness of a distribution and calculate the five-number summary (minimum, Q1, median, Q3, maximum) using boxplot data. This problem explains how skewness affects distribution and is suitable for students in Grades 8-10.

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