Number of days required to settle each invoice. Using the data given below, create a frequency polygon and Ogive curve.

Steps to Solve

1. Organize the Data

   We start by summarizing the data into intervals and their corresponding frequencies:

   • 1-3 days: 10 invoices
   • 3-5 days: 20 invoices
   • 5-7 days: 50 invoices
   • 7-9 days: 30 invoices

2. Calculate Class Midpoints

   For each interval, calculate the class midpoint, which will be used for plotting:

   • Midpoint for 1-3 days = $(1 + 3)/2 = 2$
   • Midpoint for 3-5 days = $(3 + 5)/2 = 4$
   • Midpoint for 5-7 days = $(5 + 7)/2 = 6$
   • Midpoint for 7-9 days = $(7 + 9)/2 = 8$

3. Create a Frequency Table

   Construct a table with midpoints and frequencies:

   Midpoint	Frequency
   2	10
   4	20
   6	50
   8	30

4. Plotting the Frequency Polygon

   On graph paper or graphing software, plot the midpoints against their frequencies, and connect the points with straight lines. You should plot the point for (0 days, 0 invoices) to start and (9 days, 0 invoices) to end the polygon.

5. Calculate Cumulative Frequencies

   To create an Ogive, calculate the cumulative frequency:

   • Up to 3 days: 10
   • Up to 5 days: $10 + 20 = 30$
   • Up to 7 days: $30 + 50 = 80$
   • Up to 9 days: $80 + 30 = 110$

6. Create a Cumulative Frequency Table

   Class Interval	Cumulative Frequency
   1-3	10
   3-5	30
   5-7	80
   7-9	110

7. Plotting the Ogive

   Similar to the frequency polygon, plot the cumulative frequency against the upper class boundaries. Connect the points with straight lines. Include the point (9 days, 110 invoices) at the top right.