Question 1: When plotting a cumulative frequency graph, ensure that the points are connected with smooth lines and that the axes are correctly scaled. The cumulative frequency at a given point is found by adding the frequencies from the lowest class up to that point.

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Question 1: Plot the cumulative frequency points for the data: 5, 8, 12, 16, 20, 25, 30. Connect the points smoothly on the grid provided.

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Question 2: The cumulative frequency data for a set of exam scores is: 10, 18, 24, 30, 36, 42. Draw the corresponding cumulative frequency graph.

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Question 3: A student plots the cumulative frequency graph but mistakenly reverses the scale on the y-axis. How would this error affect the interpretation of the graph?

Answer: Reversing the scale would invert the data, making it appear that lower cumulative frequencies are higher and vice versa, leading to incorrect conclusions about the distribution.

Question 4: Identify the common plotting error if the points on a cumulative frequency graph are not connected with a smooth line but are instead joined with straight segments.

Answer: Incorrectly connecting points with straight lines instead of a smooth curve can suggest non-continuous data or misrepresent the true distribution.

Question 5: Given the following cumulative frequencies at class boundaries: 0, 5, 12, 20, 30, 42, plot these points and explain how to check if the graph is correctly scaled.

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Question 6: A student mistakenly plots the cumulative frequency at 4, 8, 11, 15, 19 instead of the correct values. What is the likely cause of this error?

Answer: Possible miscalculation in cumulative addition or reading incorrect data points from the frequency table.

Question 7: Construct a cumulative frequency graph for the data: 3, 7, 10, 14, 18, 22, ensuring proper scaling and smooth connection of points.

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Question 8: Explain why it is important to start the y-axis at zero when plotting cumulative frequency graphs.

Answer: Starting at zero ensures the graph accurately reflects the total accumulation of data and prevents misleading interpretations of the distribution.

Question 9: A graph shows a sudden jump in the cumulative frequency between two points, but the data suggests a smooth increase. What mistake might have been made?

Answer: The points were joined with straight segments instead of a smooth curve, or the data was incorrectly recorded.

Question 10: Using a different scale on the y-axis (e.g., 0, 10, 20, 40), how does this affect the accuracy of interpreting the cumulative frequency graph?

Answer: Changing the scale can distort the shape and apparent distribution, making visual interpretation less accurate unless properly accounted for.

Question 11: Identify and correct the plotting error in the following scenario: the student plots points but forgets to connect them, resulting in a disconnected set of points.

Answer: The graph should be connected with a smooth or straight line to accurately represent the cumulative frequency distribution.