Question

Calculate the sample standard deviation and sample variance 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 MinuteClass Frequency 61 - 66 12 67 - 72 3 73 - 78 9 79 - 84 11 85 - 90 13

Answer 1

The below statistical formulas are employed to find the standard deviation for the frequency distribution table data set

The grouped data information provided, with the corresponding frequencies is shown in the table below:

Classes	Frequency (f)
61-66	12
67-72	3
73-78	9
79-84	11
85-90	13

For each of the grouped classes we need to compute the midpoint (MM), by calculating the average between the lower and upper value of the class. Then, the following table si obtained:

Classes	M	f	M · f	M2 · f
61-66	63.5	12	762	48387
67-72	69.5	3	208.5	14490.75
73-78	75.5	9	679.5	51302.25
79-84	81.5	11	896.5	73064.75
85-90	87.5	13	1137.5	99531.25
	Sum =	48	3684	286776

SD = 9.259

Variance = 85.723