Question

Professor Smith took a sample of 196 students from her morning class and a sample of 162 students from her evening class. On Exam 1, all those sampled from the morning class got a 65 while those sampled from the evening class averaged a 72 with a variance of 173.f Professor Smith combines these two samples. Question 2 What is the combined Exam 1 average? Question 3A What is the combined Exam 1median? Question 3B What is the shape of the combined Exam 1 grade distribution? Question 4What is the combined Exam 1standard deviation? HWNotes | HWExcelDirections HW FuelData

PS. Answers with 4 digits

Answer 1

2)combined average=(196*65+162*72)/(196+162)=68.1676

3A)median =65

3B)shape of combined exam I grade distribution: right skewed

4)

here $\sum$x2² =(n-1)*s²+($\sum$x2))²/n =(162-1)*173+(72*162)²/162=867661

hence combined sum =$\sum$x =65*196+72*162=24404

also sum of square $\sum$x² =$\sum$x1² +$\sum$x2² =196*65²+27885=855985

hence std deviation =sqrt( ($\sum$x²-( $\sum$x)²/n)/(n-1))=9.4970