The data represent the number of ounces of water that 26 students drank before donating blood: 8, 8, 8, 16, 16, 16, 32, 32, 32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 64, 80, 80, 80, 80, 88, 88, 88. Find first quartile

To find the first quartile (Q1) of a data set, we follow these steps:

### Step 1: Organize the data in ascending order.
Here is the sorted list of the number of ounces of water:

8, 8, 8, 16, 16, 16, 32, 32, 32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 64, 80, 80, 80, 80, 88, 88, 88

### Step 2: Calculate the position of the first quartile.
The formula for the position of Q1 in a sorted data set is:
\[
Q1 = \frac{(n + 1)}{4}
\]
where \(n\) is the number of data points.

For this data set, \(n = 26\). Plugging this into the formula:
\[
Q1 = \frac{(26 + 1)}{4} = \frac{27}{4} = 6.75
\]
This means Q1 lies between the 6th and 7th data points.

### Step 3: Find the first quartile.
- The 6th data point is 16.
- The 7th data point is 32.

Now, we interpolate between these two points. Since 6.75 is closer to the 7th value, we calculate:
\[
Q1 = 16 + (32 - 16) \times (0.75) = 16 + 16 \times 0.75 = 16 + 12 = 28
\]

So, the first quartile (Q1) is **28 ounces**.

Would you like further details or have any questions?

Here are five related questions:
1. What is the median (second quartile) of the same data set?
2. How would you find the third quartile (Q3) for this data?
3. What is the interquartile range (IQR) and how is it calculated?
4. How do outliers affect quartiles and how would you detect them in this data?
5. How would you create a box plot to visually represent the quartiles of this data set?

**Tip:** Quartiles divide a data set into four equal parts. Q1 represents the point below which 25% of the data falls.

The data represent the number of ounces of water that 26 students drank before donating blood: 8, 8, 8, 16, 16, 16, 32, 32, 32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 64, 80, 80, 80, 80, 88, 88, 88. Find first quartile.

Learn how to calculate the first quartile (Q1) of a data set representing water consumption of 26 students before donating blood. This problem involves sorting the data, using the quartile formula, and applying interpolation to find Q1 as 28 ounces. Suitable for students in Grades 6-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation