To find the lower quartile (Q1), the median (Q2), and the upper quartile (Q3), we need to organize the dataset in ascending order and then apply the quartile formula.

Step 1: Sort the data

The original dataset is: $37, 48, 40, 57, 25, 37, 98, 60, 86, 37, 93, 22$

Sorting in ascending order: $22, 25, 37, 37, 37, 40, 48, 57, 60, 86, 93, 98$

Step 2: Median (Q2)

The median is the middle value of the dataset. Since there are 12 values, the median is the average of the 6th and 7th values.

6th value: 40
7th value: 48

$\text{Median (Q2)} = \frac{40 + 48}{2} = 44$

Step 3: Lower quartile (Q1)

The lower quartile (Q1) is the median of the lower half of the data (the first 6 values): $22, 25, 37, 37, 37, 40$

The median of this subset is the average of the 3rd and 4th values: $\text{Q1} = \frac{37 + 37}{2} = 37$

Step 4: Upper quartile (Q3)

The upper quartile (Q3) is the median of the upper half of the data (the last 6 values): $48, 57, 60, 86, 93, 98$

The median of this subset is the average of the 3rd and 4th values: $\text{Q3} = \frac{60 + 86}{2} = 73$

Final Results:

• Lower quartile (Q1) = 37
• Median (Q2) = 44
• Upper quartile (Q3) = 73

Would you like more details or explanations?

Related Questions:

1. What is the interquartile range (IQR) and how is it calculated?
2. How do outliers affect quartiles in a dataset?
3. What are the uses of quartiles in statistics?
4. Can you explain how to find quartiles in datasets with an odd number of values?
5. What are other measures of central tendency besides the median?

Tip:

When calculating quartiles for larger datasets, visual tools like box plots can help summarize data distributions easily.