Question 1
Paper 2Hard6 marksA city council is estimating the number of potholes on a typical 1 km road segment. It has two samples, each containing 40 segments.
The app sample consists of segments for which residents submitted reports during one month. Reports were grouped by segment, but the counts were not independently checked. The inspection sample was selected by stratified random sampling, in proportion to the number of segments in each road class. Inspectors counted and checked the potholes.
Figure 1 shows box-and-whisker plots of the recorded number of potholes per segment. Inspection confirmed that the segment represented by the value 14 had 14 distinct potholes. The value 18 in the app sample has not been checked.
For this question, a value is an outlier if it is more than beyond the nearest quartile.
The council proposes deleting both marked high values as recording errors and using the remaining app sample to estimate the typical number of potholes per city segment.
For each sample, calculate the upper outlier fence and determine whether its marked high value is an outlier.
Using your result from part (a), evaluate the council’s proposal. Recommend a defensible way to estimate the typical number of potholes, using evidence from Figure 1 and the sampling information.