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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Dot Plot
A dot plot is a graphical representation where each data point is represented by a dot above its corresponding value on a number line. To find the median, we need to follow a specific process.
Step 3:: Order the Data
First, arrange all the data points in ascending order. This helps us identify the middle value(s).
Step 4:: Determine the Number of Data Points
Let's call this number $$n$$.
Count the total number of data points in the dot plot.
Step 5:: Median Calculation
- If $$n$$ is odd: The median is the middle value
- If n is even: The median is the average of the two middle values
Step 6:: Finding the Median
Median = $$\frac{x_{\frac{n}{2}} + x_{\frac{n}{2}+1}}{2}$$ (average of two middle values)
- For an odd number of data points: - For an even number of data points: Example: Let's say we have a dot plot with values: 2, 3, 3, 4, 4, 4, 5, 5, 6
Step 7:: Practical Application
- Total data points $$n = 9$$ (odd number)
- Middle position is \frac{9 + 1}{2} = 5 - The 5th value is 4 - Therefore, the median is 4
Final Answer
1. Counting the total number of data points 2. Identifying the middle value(s) 3. If odd number of points, take the middle value 4. If even number of points, take the average of the two middle values
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