Cumulative Frequency Graph Analysis

00:00 8 marks

The cumulative frequency table below summarizes the test scores of 200 students. Use this information to answer the following questions.

| Score | Cumulative Frequency |
|——-|———————-|
| 40 | 20 |
| 50 | 60 |
| 60 | 120 |
| 70 | 160 |
| 80 | 190 |
| 90 | 200 |

Part a

5 minutes 4 marks

Question

Draw a cumulative frequency graph (ogive) based on the data provided in the table below:

| Score | Cumulative Frequency |
|——-|———————-|
| 40 | 20 |
| 50 | 60 |
| 60 | 120 |
| 70 | 160 |
| 80 | 190 |
| 90 | 200 |

Ensure that the x-axis is labeled ‘Test Scores’, and the y-axis is labeled ‘Cumulative Frequency’. Choose and use appropriate scales for both axes to effectively display the data. Plot the points accurately and connect them with a smooth curve to form the ogive.

Hint Hint

Hint

Use graph paper to plot the points from the table, ensuring correct axis labels and scales. Connect the points in order to create the ogive.

Answer Answer
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Answer Answer

Complete Answer

An ogive accurately plotted with the points (40,20), (50,60), (60,120), (70,160), (80,190), and (90,200), with clearly labeled axes (‘Test Scores’ and ‘Cumulative Frequency’) and a smooth, increasing curve connecting the points.

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Part b

5 minutes 4 marks

Question

Using the ogive you constructed in part (a), estimate the first quartile (Q1), the median (Q2), and the third quartile (Q3) of the test scores. On your ogive, clearly show how you located these values, including any horizontal and vertical lines drawn. State your estimated values for Q1, Q2, and Q3. (Note: The total frequency is 200, so Q1 corresponds to a cumulative frequency of 50, Q2 to 100, and Q3 to 150.)

Hint Hint

Hint

On your ogive, find the cumulative frequencies 50, 100, and 150 on the y-axis. Trace horizontally from each of these points to the ogive curve, and then vertically down to the x-axis to estimate Q1, Q2, and Q3. For more precise estimates, use linear interpolation between the relevant data points on the ogive.

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Complete Answer

Estimated quartiles from the ogive using linear interpolation are: Q1 \approx 47.5, Q2 \approx 56.7, Q3 \approx 67.5. These values should be clearly derived and indicated with lines on the drawn ogive.

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