The following stem-and-leaf plot represents the prices in dollars of general admission tickets for the last 2626 concerts at one venue. Use the data provided to find the quartiles.

Ticket Prices in Dollars

Stem				Leaves				

3	0	0	2	6	7	8		

4	4	5	5	6	7			

5	1	1	2	2	4	5	7	

6	0	2	2	3	4	5	8	8

To find the quartiles of the ticket prices based on the stem-and-leaf plot, we'll follow these steps:

1. **List the data values** in ascending order from the stem-and-leaf plot.
2. **Determine the positions** of the first quartile (\(Q_1\)), the median (\(Q_2\)), and the third quartile (\(Q_3\)).

### Step 1: List the Data Values

From the stem-and-leaf plot, the ticket prices are:

- **Stem 3:** 30, 30, 32, 36, 37, 38
- **Stem 4:** 44, 45, 45, 46, 47
- **Stem 5:** 51, 51, 52, 52, 54, 55, 57
- **Stem 6:** 60, 62, 62, 63, 64, 65, 68, 68

Now, list all these values in ascending order:

\[ 30, 30, 32, 36, 37, 38, 44, 45, 45, 46, 47, 51, 51, 52, 52, 54, 55, 57, 60, 62, 62, 63, 64, 65, 68, 68 \]

### Step 2: Determine the Quartiles

There are 26 data points. The quartiles divide the data into four equal parts.

#### Median (\(Q_2\)):

- Position of the median (Middle value):
\[
\text{Position} = \frac{26 + 1}{2} = 13.5
\]
Since 13.5 is not an integer, the median is the average of the 13th and 14th values.

- 13th value: 51
- 14th value: 52

\[
Q_2 = \frac{51 + 52}{2} = 51.5
\]

So, \( Q_2 \) (median) is 51.5.

#### First Quartile (\(Q_1\)):

- Position of the first quartile:
\[
\text{Position} = \frac{26 + 1}{4} = 6.75
\]
Round up to the 7th value.

- 7th value: 44

So, \( Q_1 \) is 44.

#### Third Quartile (\(Q_3\)):

- Position of the third quartile:
\[
\text{Position} = 3 \times \frac{26 + 1}{4} = 20.25
\]
Round up to the 21st value.

- 21st value: 62

So, \( Q_3 \) is 62.

### Summary of Quartiles
- **First Quartile \( Q_1 \):** 44
- **Median \( Q_2 \):** 51.5
- **Third Quartile \( Q_3 \):** 62

Would you like further details or have any questions?

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Here are 5 related questions you might find interesting:
1. How can you interpret the interquartile range (IQR) from this data?
2. What is the significance of quartiles in statistical analysis?
3. How do quartiles relate to box plots?
4. How would outliers affect the quartiles in a data set?
5. Can you calculate the range and variance for this data set?

**Tip:** Quartiles are particularly useful in identifying the spread and central tendency of data, especially in understanding the distribution of values within a data set.

Learn how to find quartiles from a stem-and-leaf plot of ticket prices for concerts. This detailed solution covers steps to list data values, determine quartile positions, and calculate quartile values. Suitable for high school students studying descriptive statistics.

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