Question

The Thomas Supply Company Inc. is a distributor of gas-powered generators. As with any business, the length of time customers take to pay their invoices is important. Listed below, arranged from smallest to largest, is the time, in days, for a sample of the Thomas Supply Company Inc. invoices.13 13 13 20 26 28 30 34 34 34 35 35 36 37 38

41 41 41 45 46 47 47 49 52 54 54 56 62 67 82(Round your answer to 2 decimal places.)a. Determine the first and third quartiles.
b. Determine the second decile and the eight decile.c. Determine the 67th percentile.

Answer 1

To calculate the quartiles, deciles, and percentiles for a set of invoice payment times, we rank the data and apply formulas to find the respective positions in the data set. Afterward, we interpolate between data points if necessary to extract the correct values based on the position calculations.

Step-by-step explanation:

To determine the first and third quartiles, the second decile, and the 67th percentile for a set of data representing the number of days Thomas Supply Company Inc.'s customers take to pay their invoices, we need to follow a series of steps for each part of the question. The provided data set is arranged from smallest to largest. Given that there are 30 data points in the sample, we can employ the following methods for the calculations:

• Quartiles: To find the quartiles, we will divide the data into four equal parts. The first quartile (Q1) is the median of the first half of the data, the second quartile (Q2) is the overall median, and the third quartile (Q3) is the median of the second half of the data.
• Deciles: Deciles are similar to quartiles but divide the data into ten equal parts. The second decile (D2) is the value below which 20% of the data lies, and the eighth decile (D8) is the value below which 80% of the data lies.
• Percentiles: The 67th percentile (P67) is the value below which 67% of the data falls.

To find the quartiles, we calculate the position in the data set using the formula: Position = (n+1) * p, where n is the sample size and p is the desired percentile in decimal form.

For the first quartile (Q1): Position = (30+1) * 0.25 = 7.75, which falls between the 7th and 8th value, so we average them to find Q1. Similarly, for the third quartile (Q3), we find the position using a p value of 0.75.

To find the second decile (D2), we use p = 0.2, and for the eighth decile (D8), we use p = 0.8. We follow the same method to interpolate between the two nearest data points if the position is not a whole number.

For the 67th percentile (P67), we use p = 0.67 and interpolate between the corresponding data points to find the value.