1. **Problem Statement:** Draw a frequency polygon based on the given data set. 2. **Understanding Frequency Polygon:** A frequency polygon is a graph that shows the frequencies of different classes or values by connecting the midpoints of the tops of the bars of a histogram with straight lines. 3. **Step 1: Organize the Data** - List the unique values in ascending order. - Count the frequency of each value. 4. **Step 2: Calculate Frequencies** - 27: 1 - 48: 3 - 54: 1 - 57: 1 - 59: 2 - 60: 1 - 61: 2 - 62: 1 - 63: 1 - 64: 2 - 65: 2 - 66: 2 - 67: 3 - 68: 4 - 71: 2 - 72: 2 - 76: 2 - 78: 1 - 80: 1 - 86: 1 - 94: 1 5. **Step 3: Plot the Frequency Polygon** - On the x-axis, plot the unique values. - On the y-axis, plot the corresponding frequencies. - Connect the points with straight lines. 6. **Formula:** Frequency polygon points are $(x_i, f_i)$ where $x_i$ is the data value and $f_i$ is its frequency. 7. **Explanation:** This method helps visualize the distribution of data points clearly. **Final Answer:** The frequency polygon is the graph connecting points $(27,1)$, $(48,3)$, $(54,1)$, $(57,1)$, $(59,2)$, $(60,1)$, $(61,2)$, $(62,1)$, $(63,1)$, $(64,2)$, $(65,2)$, $(66,2)$, $(67,3)$, $(68,4)$, $(71,2)$, $(72,2)$, $(76,2)$, $(78,1)$, $(80,1)$, $(86,1)$, $(94,1)$ with straight lines.