Question

Letter Grade C Percent (a) What is the formula you would use to find the standard. deviation of only the Female scores? And what is the stan- dard deviation? Time Name Arya Jaime Cersei Gender Female 3. 70 25 60 30 Male Female Female E 80 35 D+ 65 30 Ygritte Bran Bronn Samwell Brienne A 95 40 Male Male F 20 15 80 40 (b) Would you use the same formula if I had asked for the scores for Bran, Tyrion, Bronn, Jaime, Samwell, Petyr, and Eddard, a not so random sample picked from the pop- ulation? If you think it is the same write "same" and explain why you think this is the case. If you think different, write out that formula, Male Female Male Male C+ 75 35 A 95 5 Petyr Eddard Daenerys Sansa Tyrion Missandei C 70 40 80 85 30 Female Female B B+ 40 A 90 35 Male 100 and please give your justification. Female A 35

Answer 1

(a)population standard deviation=sqrt(sum((x-mean)²/n))=sqrt(771.4287/7)=10.4978

here we used population standard deviations

S.N.	female(x)	x-mean	(x-mean)2
1	70	-9.29	86.3041
2	80	0.71	0.5041
3	65	-14.29	204.2041
4	75	-4.29	18.4041
5	80	0.71	0.5041
6	85	5.71	32.6041
7	100	20.71	428.9041
sum=	555	-0.03	771.4287
mean=	555/7=79.29

(b)different, here we should use sample standard deviation and  

sample standard deviation=sqrt(sum((x-mean)²/(n-)))=sqrt(4292.8572//(7-1))=26.75

S.N.	male(x)	x-mean	(x-mean)2
1	95	22.14	490.1796
2	20	-52.86	2794.1796
3	90	17.14	293.7796
4	60	-12.86	165.3796
5	80	7.14	50.9796
6	95	22.14	490.1796
7	70	-2.86	8.1796
sum=	510	-0.02	4292.8572
mean=	510/7=72.86