Question

Days on the Market
Dave Supien is a manager at a real estate agency in lower Delaware and has been looking at the current housing market. He established that the market conditions have been recovering during the past few years and wanted to continue his analysis. The following data shows the number of days a house has been on the market for Sussex County during the past year.

38 94 106 32 70 115 17 34 76 100 48
62 40 77 39 51 68 10 87 178 69

Find the following.
A) The percentile of days between the second and third positions.
B) The percentile rank a house that has been on the market for 106 days.
C) The box–and–whisker plot.
D) The five–number summary.

Answer 1

Data	sl no.
10	1
17	2
32	3
34	4
38	5
39	6
40	7
48	8
51	9
62	10
68	11
69	12
70	13
76	14
77	15
87	16
94	17
100	18
106	19
115	20
178	21

A) The percentile of days between the second and third positions.

Percentile of 2nd position is = (2/21)*100 = 9.52%

Percentile of 3rd position is = (3/21)*100 = 14.29%

percentile rank of days between 2nd and 3rd = (9.52+14.29)/2 = 11.91%

Percentile of days in between 2nd and 3rd = 0.1191*21 = 2.5th data

= (17+32)/2 = 24.5 days.

B) The percentile rank a house that has been on the market for 106 days.

Number of values below 106 days = 18

Percentile rank = (18/21)*100 = 85.71%

C) The box–and–whisker plot.

D) The five–number summary.

Min = 10

Q1 = (21+1)/4 th data = 5.5 th data

= Average (5th and 6th ) data

= (38+39)/2 = 38.5

Median = (21+1)/2 th data = 11th data = 68

Q3 = (21+1) *3/4 th data = 16.5 th data

= Average of (16th snd 17 th)

= (87+94) / 2 = 90.5

Max = 178

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