Question

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

Heart Rates in Beats per Minute

Class	Frequency
61 - 66	13
67 - 72	9
73 - 78	5
79 - 84	3
885 - 90	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)
61-66	13	63.5	825.5	52419.25
67-72	9	69.5	625.5	43472.25
73-78	5	75.5	377.5	28501.25
79-84	3	81.5	244.5	19926.75
85-90	6	87.5	525	45937.5
	n=36		∑f⋅x=2598	∑f⋅x2=190257

Sample Variance S2=∑f⋅x2-(∑f⋅x)2nn-1

=190257-(2598)236/35

=190257-187489/35

=276835

=79.0857

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

=√190257-(2598)23635

=√190257-187489/35

=√2768/35

=√79.0857

=8.893