Question

3. Stem-and-leaf displays can be used to compare distributions for two groups using a back-to-back stem- and-leaf display. In such a display, one group is shown on the left side of the stems, and the other group is shown on the right side. When the leaves are ordered, the leaves incrcasc as one moves away from the stems. Thc following stem-and-leaf display shows the moncy carned per tournament entered for the top 30 money winners in the 2008-09 Professional Bowlers Association men's tour and for the top 21 money winners in the 2008-09 Professional Bowlers Association women's tour,

Answer 1

1. Yes, Among Women group after earnings of $2600 and starting from $3000,it tend to make more money per tournament played than other tours. Since it is more than average earning per tournament.
2. For Women Group earning per tournament is $2995.24     and for Men Group is $4046.67.
3. No. There is more spread in Women group as compare with Men Group. ( It will get by drawing a normal curve either sides of two groups or even we can use standard deviation or coefficient of variation for both groups , then least among two groups get less spread or more consistent).
4. Yes in both groups having outliers. They can be find using the following rule (Q₁-1.5 IQR> outlier > (Q₃+1.5IQR) beyond this range one can consider as outlier. By using this rule for Women group ( - $700 , $6500) there is one outlier i.e $7500. On the other hand in Men group ($350, $7150) there two outliers and they are $8700, $9500. Here Q₁ is First Quartile and Q₃ is the third Quartile and IQR means Inter Quartile Range (IQR= Q₃-Q₁).