To find the median, first quartile (Q1), and third quartile (Q3) from this list, we follow these steps:

Step 1: Organize the Data

The list is already sorted in ascending order:

1, 9, 10, 12, 13, 14, 20, 21, 26, 27, 28, 30, 32, 35, 36, 36, 37, 40, 40, 42, 42, 45, 47, 48, 50, 51, 52, 52, 53, 57

There are 30 data points in total.

Step 2: Median

The median is the middle value of the dataset. Since there are 30 numbers (an even amount), the median will be the average of the 15th and 16th values.

• 15th value = 36
• 16th value = 36

So, the median is: $\text{Median} = \frac{36 + 36}{2} = 36$

Step 3: First Quartile (Q1)

The first quartile (Q1) is the median of the lower half of the data, which includes the first 15 numbers (from the 1st to the 15th value): $1, 9, 10, 12, 13, 14, 20, 21, 26, 27, 28, 30, 32, 35, 36$

The median of this subset is the 8th value: $Q1 = 21$

Step 4: Third Quartile (Q3)

The third quartile (Q3) is the median of the upper half of the data, which includes the last 15 numbers (from the 16th to the 30th value): $36, 37, 40, 40, 42, 42, 45, 47, 48, 50, 51, 52, 52, 53, 57$

The median of this subset is the 23rd value: $Q3 = 47$

Summary:

• Median (Q2): 36
• First Quartile (Q1): 21
• Third Quartile (Q3): 47

Would you like any details or have any questions?

Here are 5 related questions for further practice:

1. How do you interpret the interquartile range (IQR) from a box plot?
2. What is the relationship between the median and the mean in a symmetric distribution?
3. How do you identify outliers using a box and whisker plot?
4. Can you explain the significance of the whiskers in a box plot?
5. How does skewness affect the shape of a box and whisker plot?

Tip: The interquartile range (IQR) is a good measure of variability that is resistant to outliers, as it focuses on the middle 50% of the data.