For a box and whisker diagram find the median, first quartile and third quartile from this list:
1.	1
2.	9
3.	10
4.	12
5.	13
6.	14
7.	20
8.	21
9.	26
10.	27
11.	28
12.	30
13.	32
14.	35
15.	36
16.	36
17.	37
18.	40
19.	40
20.	42
21.	42
22.	45
23.	47
24.	48
25.	50
26.	51
27.	52
28.	52
29.	53
30.	57


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.

For a box and whisker diagram, find the median, first quartile, and third quartile from this list: 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.

Learn how to find the median, first quartile (Q1), and third quartile (Q3) for a given dataset used in a box and whisker plot. This problem uses a list of 30 numbers and covers key statistical concepts, including the median, Q1, and Q3. Suitable for students in Grades 7-10.

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