Question

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6.
Below are the times (in days) it takes for a sample of 18 customers from Jack's computer store to pay their invoices. 19, 15, 43, 39, 35, 31, 27, 22, 18, 14, 26, 26, 26, 21, 21, 21, 17, 17 Draw the frequency polygon for these data using an initial class boundary of 13.5, an ending class boundary of 48.5 and 5 classes of equal width. Note that you can add or remove classes from the figure. Label each class with its midpoint. Frequency 8+ 7 6+ S 4+ 3+ time in care i

Answer 1

A sample of 18 customers from Jack's computer store to pay their invoices are given as:

NOTE: I have rearranged the data in ascending order as it will help us in calculating the frequency easily.

14, 15, 17, 17, 18, 19, 21, 21, 21, 22, 26, 26, 26, 27, 31, 35, 39, 43

Using an initial class boundary of 13.5 and an ending class boundary of 48.5 with a width of 5 classes, we form the following table:

Interval	Midpoint	Frequency
13.5 - 18.5	16	5
18.5 - 23.5	21	5
23.5 - 28.5	26	4
28.5 - 33.5	31	1
33.5 - 38.5	36	1
38.5 - 43.5	41	2
43.5 - 48.5	46	0

The frequency is found out by checking for the numbers that lie in that interval.

The midpoint column is formed by finding the mid point of the interval column. For example, the midpoint of the interval 13.5 - 18.5 is found by $\frac{13.5+18.5}{2}=16$

The steps to draw a frequency polygon is :

1. Draw the X and Y axis.

2. The midpoint is drawn on the X axis and the frequency is drawn on the Y axis.

3. Then, we plot the values of midpoint against the frequency.

4. Join the points through a line.

5. Extend the first and the last point towards the X axis line.

6. The graph we have now is a frequency polygon.

I have attached the graph i have drawn below.

13 12 Il 10 9 2 7 6 5 Frequency 4 3 2 - H + 16 21 26 31 36 46 Time (in days)