https://file.aiquickdraw.com/mathbot/file/1726373736141gkyotdc2.jpeg

Let's solve the problems shown in the image:

### 1. Dissolved Oxygen Concentration:
The six values of dissolved oxygen concentration (in mg/L) are:
\[
8.8, 7.1, 7.2, 8.2, 7.6, 8.6
\]

### 2. Plot a Graph:
To plot the graph, you can create a simple line or bar graph with the sample numbers (1 through 6) on the x-axis and the dissolved oxygen concentrations on the y-axis. Each sample corresponds to a concentration value.

### 3. Find the Mean:
To calculate the mean (average) of the samples:

\[
\text{Mean} = \frac{\text{Sum of the values}}{\text{Number of values}}
= \frac{8.8 + 7.1 + 7.2 + 8.2 + 7.6 + 8.6}{6}
\]

Let me calculate the mean first.

### 4. Find the Variance:
Variance is calculated as the average of the squared differences from the mean:
\[
\text{Variance} = \frac{\sum_{i=1}^{n} (x_i - \mu)^2}{n}
\]
where \( x_i \) are the data points and \( \mu \) is the mean.

I'll calculate the mean and variance now.### Results:
3. **Mean**: The mean of the dissolved oxygen concentrations is approximately **7.92 mg/L**.
4. **Variance**: The variance of the dissolved oxygen concentrations is approximately **0.435 mg/L²**.

Would you like more details or explanations on any part of the solution? 

Here are five related questions for further exploration:
1. What is the standard deviation of the data, and how is it related to variance?
2. How would the mean and variance change if another sample were added with a value of 7.5 mg/L?
3. How would the graph look if we plotted the median instead of the mean?
4. Can you describe the relationship between variance and consistency in the data set?
5. How would the results change if you removed an outlier from the data?

**Tip**: Remember that variance gives you an idea of how spread out the values are from the mean. The square root of variance is called the standard deviation, which is easier to interpret in the same units as the data.

A student collects a series of six groundwater samples from a well. She measures the dissolved oxygen concentration in mg/L as 8.8, 7.1, 7.2, 8.2, 7.6, 8.6. The problem asks to plot a graph based on the given values, find the mean, and find the variance.

This problem involves calculating the mean and variance of dissolved oxygen concentration values from groundwater samples. Learn how to plot the graph, calculate the mean of the values, and determine the variance. Suitable for students in Grades 7-10.

Math Problem Statement

Solution

1. Dissolved Oxygen Concentration:

2. Plot a Graph:

3. Find the Mean:

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