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To calculate the **descriptive statistics** for the data in row 2, which are the temperatures recorded over 24 days, we will follow these steps:

The temperatures are:
\[38, 45, 49, 47, 52, 54, 48, 51, 50, 44, 51, 50, 54, 49, 50, 50, 46, 49, 50, 45, 49, 51, 50, 50\]

### (a) **Sample Mean**:
The sample mean \(\bar{x}\) is the average of all the data points.
\[
\bar{x} = \frac{\sum x_i}{n}
\]
where \(x_i\) are the data points and \(n\) is the number of observations (24 in this case).

\[
\bar{x} = \frac{38 + 45 + 49 + 47 + 52 + 54 + 48 + 51 + 50 + 44 + 51 + 50 + 54 + 49 + 50 + 50 + 46 + 49 + 50 + 45 + 49 + 51 + 50 + 50}{24}
\]

Summing these values gives:
\[
\sum x_i = 1182
\]
Thus, the mean is:
\[
\bar{x} = \frac{1182}{24} \approx 49.25
\]
So, the **mean** is **49.3°F** (rounded to 1 decimal place).

### (b) **Sample Variance**:
The sample variance \(s^2\) is calculated as:
\[
s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}
\]
We already have \(\bar{x} = 49.25\), so we need to compute the squared differences from the mean for each data point, sum them up, and divide by \(n-1 = 23\).

- For each data point \(x_i\), calculate \((x_i - 49.25)^2\).
- Sum the squared differences.

\[
\sum (x_i - 49.25)^2 \approx 185.6875
\]

So, the variance is:
\[
s^2 = \frac{185.6875}{23} \approx 8.07
\]
Thus, the **variance** is approximately **8.1** (rounded to 1 decimal place).

### (c) **Sample Standard Deviation**:
The sample standard deviation \(s\) is the square root of the variance:
\[
s = \sqrt{s^2} = \sqrt{8.07} \approx 2.84
\]
So, the **standard deviation** is approximately **2.8°F** (rounded to 1 decimal place).

### Summary:
- (a) Sample Mean: **49.3°F**
- (b) Sample Variance: **8.1**
- (c) Sample Standard Deviation: **2.8°F**

Would you like further details or clarifications?

Here are some additional questions that expand on this:
1. How do outliers affect the mean and standard deviation?
2. Can you explain why we use \(n-1\) in the sample variance formula?
3. What is the significance of standard deviation in this dataset?
4. How would the calculations change if more days were added to the dataset?
5. Can we consider these temperatures normally distributed?

**Tip**: Variance is a measure of how spread out the numbers in a dataset are, while standard deviation is the square root of variance and provides a measure of spread in the same units as the data.

Calculate descriptive statistics for the temperatures (in °F) of effluent discharge from a sewage treatment facility recorded over 24 consecutive days.

This problem involves calculating the sample mean, variance, and standard deviation for temperatures recorded at a sewage treatment facility over 24 days. The solution covers key concepts in descriptive statistics and applies formulas for central tendency and spread.

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