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 27 31 34 34 34 35 35 36 37 38 41 41 41 45 47 47 47 50 51 53 54 56 62 67 82 (Round your answers to 2 decimal places.)

Determine the first and third quartiles.

Determine the second decile and the eighth decile.

Determine the 67th percentile.

Answer 1

There are many methods of finding quartiles /percentiles and deciles, but if it is required accurate to 2 decimal places, then we find the position index first = (% / 100) * (N + 1), where N is the total observations

Assume we get a value 10.3, then the required percentile = 10th Value + 0.3(11th Value - 10th value)

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Arranging the values in ascending order we have

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
13	13	13	20	26	27	31	34	34	34	35	35	36	37	38	41	41	41	45	47	47	47	50	51	53	54	56	62	67	82

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(a) The first quartile is 25% of the data

The position index, n = (25 / 100) * 31 = 7.75 = 7th Value + 0.75 (8th value - 7th Value) = 31 + 0.75 * (34 - 31) = 33.25

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(b) The third quartile is 75% of the data

The position index, n = (75 / 100) * 31 = 23.25 = 23rd Value + 0.25 (24th value - 23th Value) = 50 + 0.25 * (51 - 50) = 50.25

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(c) The second decile is 20% of the data

The position index, n = (20 / 100) * 31 = 6.2 = 6th Value + 0.2 (7th value - 6th Value) = 27 + 0.2 * (31 - 27) = 27.80

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(d) The eighth decile is 80% of the data

The position index, n = (80 / 100) * 31 = 24.8 = 24th Value + 0.8 (25th value - 24th Value) = 51 + 0.8 * (53 - 51) = 52.60

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(e) The 67th percentile

The position index, n = (67 / 100) * 31 = 20.77 = 20th Value + 0.77 (21st value - 20th Value) = 47 + 0.77 * (47 - 47) = 47.00

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