Question

Sample SAT scores for eight males and eight females are listed

Male SAT Scores:     1059    1328    1175    1123    923      1017    1214    1042

Female SAT Scores: 1226    965      841      1053    1056    1393    1312    1222   

(a) Find the range, variance, and standard deviation for each data set.

(b) Interpret the results

Answer 1

a) Range: Sort the values from increasing to decreasing order. Subtract the highest value from the smallest value

Male SAT Scores:	Female SAT Scores:
923	841
1017	965
1042	1053
1059	1056
1123	1222
1175	1226
1214	1312
1328	1393

Male SAT Scores: Range = 1328-923 = 405

Female SAT Scores: Range = 1393-841 = 552

Variance=sum((Xi-Xavg)^2)/n-1

Average of Male SAT Scores = 8881/8= 1110.13

Average of Female SAT Scores = 9068/8= 1133.5

Standard deviation = Sqrt of Variance

Male SAT Scores:	sum((Xi-Xavg)^2)	Female SAT Scores:	sum((Xi-Xavg)^2)
923	35017.64	841	85556.25
1017	8673.20	965	28392.25
1042	4641.70	1053	6480.25
1059	2614.28	1056	6006.25
1123	165.64	1222	7832.25
1175	4208.12	1226	8556.25
1214	10788.98	1312	31862.25
1328	47467.34	1393	67340.25
sum((Xi-Xavg)^2)	113576.88		242026.00
Var	16225.27		34575.14
SD	127.3784		185.94

b) The range, variance and standard deviation is higher for female when compared to male which shows that the female score has more variation and inconsistency when compared to male