Before the sub-prime loan crisis and the end of the “housing bubble” in 2008, the value of houses was escalating rapidly, as much as 40% a year in some areas. In an effort to track housing prices, the National Association of Realtors developed the Pending Home Sales Index (PHSI), a new leading indicator for the housing market. An index of 100 is equal to the average level of contract activity during 2001, the first year to be analyzed. The index is based on a large national sample representing about 20% of home sales. The file titled Pending contains the PHSI from December 2010 to December 2011.
a. Determine the mean and median for the PHSI from December 2010 through December 2011. Specify the shape of the PHSI’s distribution.
b. The PHSI was at 91.5 in December 2010 and it was at 100.1 in November of 2011. Determine the average monthly increase in the PHSI for this period.
c. Using your answer to part b, suggest a weighting scheme to calculate the weighted mean for the months between December 2010 and November 2011. Use the scheme to produce the weighted average of the PHSI in this time period.
d. Does the weighted average seem more appropriate here? Explain.