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.

D) The five–number summary.

Answer 1

Solution :

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

Ordering the data from least to greatest, we get:

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

D) Five number summary :
  
Minimum = 10
First Quartile Q1 = 38.5
Median = 68
Third Quartile Q3 = 90.5
Maximum = 178

=> The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers
So, the bottom half is 10 17 32 34 38 39 40 48 51 62

=> The median of these numbers Q1 is = 38.5.

=> The median is the middle number in a sorted list of numbers

=> The median of the data set is 68.

=> The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers
So, the upper half is 69 70 76 77 87 94 100 106 115 178  

=> The median of these numbers is Q3 = 90.5.