Let's go through the steps for your data analysis.

Step 1: Organize Data

The data provided is: 1, 10, 20, 30, 50, 50, 50, 60, 75, 80, 80, 80, 83, 85, 90, 90, 90, 90, 90, 90, 95, 95, 97, 99, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100

Ordered Data (from lowest to highest): 1, 10, 20, 30, 50, 50, 50, 60, 75, 80, 80, 80, 83, 85, 90, 90, 90, 90, 90, 90, 95, 95, 97, 99, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100

Step 2: Calculate Quartiles

Quartile 1 (Q1):

• Quartile 1 is the median of the first half of the data (25% of the data).
• Since there are 35 data points, we first divide the data into two halves:
  • Lower half (excluding the median of the entire dataset): 1, 10, 20, 30, 50, 50, 50, 60, 75, 80, 80, 80, 83, 85, 90, 90, 90, 90, 90, 90
  • Median of the lower half = 50 (middle value in the lower half).

Thus, Q1 = 50.

Quartile 2 (Q2):

• Quartile 2 is the median of the entire dataset, which divides it into two halves (50% of the data).
• The median position in a dataset with 35 data points is at position 18 (since 35 + 1 = 36, and 36/2 = 18).
• The 18th data point is 90.

Thus, Q2 (Median) = 90.

Quartile 3 (Q3):

• Quartile 3 is the median of the second half of the data (75% of the data).
• The second half of the data (after the median) is: 90, 90, 95, 95, 97, 99, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100
• The median of the second half is 100 (since it's the middle value in the second half).

Thus, Q3 = 100.

Step 3: Box-and-Whisker Plot

Steps to plot:

1. Minimum: The smallest value in the dataset is 1.
2. Q1 (First Quartile): The value at the first quartile is 50.
3. Median (Q2): The value at the median is 90.
4. Q3 (Third Quartile): The value at the third quartile is 100.
5. Maximum: The largest value in the dataset is 100.

These points create the "box" from Q1 to Q3, and the "whiskers" extend from the minimum value to Q1, and from Q3 to the maximum value.

Step 4: Interpretation of the Box-and-Whisker Plot

• The box shows the interquartile range (IQR), which is from Q1 (50) to Q3 (100). This represents the middle 50% of the data.
• The whiskers extend from the minimum value (1) to Q1 (50) and from Q3 (100) to the maximum value (100).
• The data is skewed right, since the median (90) is closer to Q1 (50) than to Q3 (100), and there are a lot of values concentrated at 100.

---

Final Answers:

1. Q1 (First Quartile) = 50
2. Q2 (Second Quartile, Median) = 90
3. Q3 (Third Quartile) = 100

For the Box-and-Whisker Plot:

• Minimum = 1
• Q1 = 50
• Median (Q2) = 90
• Q3 = 100
• Maximum = 100

---

Would you like to see a visual representation of the Box-and-Whisker Plot? Or do you have any questions?

---

Related Questions:

1. How would you calculate the mean and standard deviation of the dataset?
2. What is the interquartile range (IQR) and how is it interpreted?
3. How does the skewness of a data set affect its interpretation?
4. What does the Box-and-Whisker Plot tell us about the spread and concentration of the data?
5. How can you calculate percentiles using the given data?

Tip: When calculating quartiles, remember that Q1 and Q3 are the medians of the lower and upper halves of the data, respectively, and the overall median divides the data into two equal parts.