https://file.aiquickdraw.com/mathbot/file/1728629964768grqyplq3.jpg

To solve this problem using the table of temperatures (in °F) from the effluent discharge over consecutive days, we need to calculate the median, first quartile, and third quartile for the data set. Let's go step by step:

### Step 1: Collect the data from the table.
The temperatures listed in row 2 are:

\[ 28, 30, 49, 40, 40, 36, 61, 29, 41, 61, 61, 62, 62, 29, 41, 50, 44, 55, 39, 49, 49, 49, 61, 60 \]

### Step 2: Sort the data in ascending order.
Arranging the temperatures in increasing order:

\[ 28, 29, 29, 30, 36, 39, 40, 40, 41, 41, 41, 44, 49, 49, 49, 49, 50, 55, 60, 61, 61, 61, 61, 62, 62 \]

### Step 3: Calculate the median.
The median is the middle value in the data set. Since there are 24 values, the median will be the average of the 12th and 13th values:

- 12th value = 44
- 13th value = 49

Median = \( \frac{44 + 49}{2} = 46.5 \)

### Step 4: Calculate the first quartile (Q1).
The first quartile is the median of the lower half of the data (first 12 values):

Lower half: \( 28, 29, 29, 30, 36, 39, 40, 40, 41, 41, 41, 44 \)

Q1 = Median of this set, which is the average of the 6th and 7th values:

- 6th value = 39
- 7th value = 40

First Quartile (Q1) = \( \frac{39 + 40}{2} = 39.5 \)

### Step 5: Calculate the third quartile (Q3).
The third quartile is the median of the upper half of the data (last 12 values):

Upper half: \( 49, 49, 49, 49, 50, 55, 60, 61, 61, 61, 61, 62 \)

Q3 = Median of this set, which is the average of the 6th and 7th values:

- 6th value = 55
- 7th value = 60

Third Quartile (Q3) = \( \frac{55 + 60}{2} = 57.5 \)

### Final Results:
- (a) Median = **46.5**
- (b) First Quartile (Q1) = **39.5**
- (c) Third Quartile (Q3) = **57.5**

Do you need further clarifications, or should we expand on any part of the explanation?

---

Here are 5 related questions to think about:
1. What is the Interquartile Range (IQR) for this data set?
2. How would an outlier be detected in this data using the IQR?
3. What effect does having repeated values (like 49 and 61) have on quartile calculations?
4. How would you graphically represent this data using a box plot?
5. What is the impact of temperature variance over time in this data set?

**Tip:** Sorting the data is crucial for accurate median and quartile calculations. Always ensure the data is correctly ordered before proceeding with these calculations.

Use the table of temperatures from a sewage treatment facility's effluent discharge on consecutive days to calculate the median, first quartile, and third quartile.

Solve for the median, first quartile, and third quartile using effluent discharge temperatures from a sewage treatment facility. This problem applies core descriptive statistics concepts, including median and quartiles, ideal for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation