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. Lower Bound Upper Bound Frequency
56 64 11
65 73 15
74 82 14
83 91 4
92 100 11

Required:
a. What is the sample standard deviation?
b. What is the sample variance?

---- sample standard deviation

---- sample variance

Step-by-step explanation:

Solving (a): The sample variance

First, we calculate the midpoint of each class (this is the average of the limits)

So, we have:

And so on

So, the table becomes:

Calculate the mean

The variance is:

So, we have:

The sample standard deviation is:

Solving (b): The sample variance

In (a), we calculate the sample variance to be:

The graph of a proportional relationship is linear, it can be positive or negative. It follows a constant rate of change.The point (0,0) which is the origin is the point that all proportion graphs follow because they arent inclusive of an y-intercept.So we have (0,0) and (3,33). We see that per every one unit the graph increased by 11. Hence it is a proportional relationship because for every one unit, it increases by 11.