Measure of Dispersion

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 MinuteClassFrequency
61 - 66	13
67 - 72	8
73 - 78	7
79 - 84	15
85 - 90	5

Answer 1

EXAMPLE for the first class 61-66

midpoint (x)= (61+66)/2 =63.5

Frequency = 13

f • x= 13 • 63.5=825.5

f•x²= 13•63.5²= 52,419.25

we repeat for all classes

then we plug the results into the formula for sample variance s²=∑fx²-[ (∑fx)² / n ] / n-1

Finally we take the square root of variance to get the standard deviation

This sample standard deviation rounded to 1 decimal place should be = 8.5