Question

Calculate the sample standard deviation and sample variance for the following frequency distribution of scores in a statistics class. If necessary, round to one more decimal place than the largest number of decimal places given in the data.

Scores

Class	Frequency
56 - 64	13
65 - 73	9
74 - 82	4
83 - 91	10
92 - 100	6

Answer 1

Solution:

Class (1)	Frequency (f) (2)	Mid value (x) (3)	f⋅x (4)=(2)×(3)	f⋅x2=(f⋅x)×(x) (5)=(4)×(3)
56-64	13	60	780	46800
65-73	9	69	621	42849
74-82	4	78	312	24336
83-91	10	87	870	75690
92-100	6	96	576	55296
	n=42		∑f⋅x=3159	∑f⋅x2=244971

Sample Standard deviation S=√∑f⋅x2-(∑f⋅x)2nn-1

=√244971-(3159)24241

=√244971-237601.928641

=√7369.071441

=√179.7334

=13.4065

Sample Standard deviation =13.4

Sample Variance S2=∑f⋅x2-(∑f⋅x)2nn-1

=244971-(3159)24241

=244971-237601.928641

=7369.071441

=179.7334

Sample Variance = 179.7