Worksheet for practicing box and whisker plot analysis with two examples and related questions.

Problem Analysis:

The image provided is a worksheet that involves analyzing a box-and-whisker plot. The task is to answer several questions based on the given box-and-whisker plot. Below, I will solve each question step by step and explain the solution.

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Box-and-Whisker Plot Recap:

A box-and-whisker plot (also known as a box plot) is a graphical representation of data that shows the following key components:
1. Minimum (Lower Extreme): The smallest value in the dataset.
2. First Quartile (Q1): The median of the lower half of the data.
3. Median (Q2): The middle value of the dataset.
4. Third Quartile (Q3): The median of the upper half of the data.
5. Maximum (Upper Extreme): The largest value in the dataset.
6. Interquartile Range (IQR): The range between Q3 and Q1 (IQR = Q3 - Q1).
7. Outliers: Data points that fall outside the whiskers (typically defined as 1.5 × IQR beyond Q1 or Q3).

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Given Box-and-Whisker Plot:

From the image:
- The minimum value is at 8.
- The maximum value is at 20.
- The first quartile (Q1) is at 10.
- The median (Q2) is at 13.
- The third quartile (Q3) is at 16.

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Solving Each Question:

#### Question 1: What is the range?
The range is the difference between the maximum and minimum values.
\[
\text{Range} = \text{Maximum} - \text{Minimum} = 20 - 8 = 12
\]
Answer: 12

#### Question 2: How many numbers are listed?
This question cannot be answered directly from the box-and-whisker plot because the plot only shows summary statistics (minimum, Q1, median, Q3, maximum). It does not provide the exact number of data points. Therefore, this question is unanswerable with the given information.

#### Question 3: What is the median?
The median is the middle value of the dataset, which is represented by the line inside the box.
\[
\text{Median} = 13
\]
Answer: 13

#### Question 4: How many numbers are between 13 and 17?
To determine how many numbers are between 13 and 17, we need to consider the positions of these values on the plot:
- The median (13) is the middle value.
- The third quartile (Q3) is at 16, which means that 25% of the data lies between 13 and 16.
- The maximum is at 20, so there are some values between 16 and 20.

However, without the exact dataset, we cannot determine the exact count of numbers between 13 and 17. This question is also unanswerable with the given information.

#### Question 5: What is the upper extreme?
The upper extreme is the maximum value in the dataset, which is represented by the right end of the whisker.
\[
\text{Upper Extreme} = 20
\]
Answer: 20

#### Question 6: What is the lower extreme?
The lower extreme is the minimum value in the dataset, which is represented by the left end of the whisker.
\[
\text{Lower Extreme} = 8
\]
Answer: 8

#### Question 7: What is the mode?
The mode is the most frequently occurring value in the dataset. However, a box-and-whisker plot does not provide information about the frequency of individual values. Therefore, this question is unanswerable with the given information.

#### Question 8: What is the target?
This term is not standard in the context of box-and-whisker plots. Without additional clarification, this question is ambiguous and unanswerable.

#### Question 9: A square represents what percentage of numbers?
In a box-and-whisker plot, the box itself (from Q1 to Q3) represents the middle 50% of the data. The square (or line) inside the box represents the median, which divides the data into two equal halves. Therefore:
\[
\text{The square represents } 50\% \text{ of the numbers.}
\]
Answer: 50%

#### Question 10: Would it be called skewed?
To determine if the data is skewed, we examine the symmetry of the box-and-whisker plot:
- The distance between the median and Q1 is smaller than the distance between the median and Q3.
- The whisker on the right side (above Q3) is longer than the whisker on the left side (below Q1).

This indicates that the data is positively skewed (skewed to the right).

Answer: Yes, it would be called skewed (positively skewed).

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Final Answers:

1. 12
2. Unanswerable
3. 13
4. Unanswerable
5. 20
6. 8
7. Unanswerable
8. Ambiguous
9. 50%
10. Yes, positively skewed

Boxed Final Answer:
\[
\boxed{12, \text{Unanswerable}, 13, \text{Unanswerable}, 20, 8, \text{Unanswerable}, \text{Ambiguous}, 50\%, \text{Yes, positively skewed}}
\]