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The diagram below shows an ogive representing the average amount that the learners

spend daily at the takeaway restaurant.
Figure 2.1: Ogive curve.
2.1 Copy and complete the following table using the ogive. You can redraw the
frequency table or print Annexure A on page 16.
Figure 2.2: Frequency table. (4)
2.2 Calculate the estimated average amount that the learners spend daily at
the takeaway restaurant.
(3)

1 answer

To complete your request, I'll need to provide a step-by-step approach on how to use the ogive to fill in the frequency table and calculate the estimated average amount spent daily. However, since I cannot view the diagram or figure you referenced, I can only guide you on the general methodology.

2.1 Completing the Frequency Table

To fill your frequency table from the ogive curve, follow these steps:

  1. Identify the cumulative frequencies from the ogive: The ogive will show you cumulative frequencies at given data points (e.g., amounts spent).

  2. Create the Frequency Table: The frequency table typically consists of class intervals (such as amount ranges) and their corresponding frequencies. The first frequency is usually the value at the first class interval.

  3. Calculate frequencies: The cumulative frequency for each class is represented on the ogive. The frequency for each class can be found by:

    • Taking the cumulative frequency at the upper boundary of the class and subtracting the cumulative frequency at the lower boundary of the class.

For example:

  • If the cumulative frequency for amounts less than $10 is 5, and the cumulative frequency for amounts less than $20 is 15, then the frequency for the class $10-$20 is:
  • \( Frequency , (10-20) = Cumulative , (20) - Cumulative , (10) = 15 - 5 = 10 \)

Example Frequency Table Format

| Amount (Range) | Cumulative Frequency | Frequency | |----------------|----------------------|-----------| | $0 - $10 | x1 | (x1-x0) | | $10 - $20 | x2 | (x2-x1) | | $20 - $30 | x3 | (x3-x2) | | $30 - $40 | x4 | (x4-x3) |

  1. Fill in the table with values from the ogive.

2.2 Calculating the Estimated Average Amount

To calculate the estimated average (mean) amount that learners spend based on your completed frequency table:

  1. Determine Midpoints (x): For each class interval, find the midpoint.

    • E.g., the midpoint for the class $10 - $20 would be \( \frac{10 + 20}{2} = 15 \).

  2. Calculate the product of midpoint and frequency: For each class, multiply the midpoint by the frequency.

    • E.g., if the frequency for $10-$20 is 10, then \( Midpoint \times Frequency = 15 \times 10 = 150 \).

  3. Sum up these products: Add all the results from step 2 for all classes.

  4. Sum the frequencies: Add all the frequencies together to get the total number of observations.

  5. Calculate the mean: \[ \text{Estimated Average} = \frac{\text{Total of (Midpoint × Frequency)}}{\text{Total Frequency}} \]

Example Calculation

Using fictitious values:

  • Total of (Midpoint × Frequency) = 300 (summed for all classes)
  • Total Frequency = 40 (for all classes)

Estimated Average = \( \frac{300}{40} = 7.5 \)

Conclusion

You can now apply this methodology with your specific values from the ogive curve and frequency table. If you have specific data points from the diagram, please share them, and I can assist with tailored calculations.