Calculate the sample mean 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 in the data.

Frequency Distribution:

| Heart Rate (beats per minute) | Frequency |
|-------------------------------|-----------|
| 60 - 69 | 8 |
| 70 - 79 | 14 |
| 80 - 89 | 20 |
| 90 - 99 | 18 |
| 100 - 109 | 10 |
| 110 - 119 | 4 |

a) Sample mean ≈ 86.9, Sample variance ≈ 99.8
b) Sample mean ≈ 92.6, Sample variance ≈ 89.4
c) Sample mean ≈ 85.3, Sample variance ≈ 102.7
d) Sample mean ≈ 88.7, Sample variance ≈ 96.2

To calculate the sample mean and sample variance for the given frequency distribution, follow the steps outlined in the answer. The sample mean is approximately 86.9 and the sample variance is approximately 99.8.

Explanation:

To calculate the sample mean and sample variance for the given frequency distribution, we need to follow these steps:

Calculate the midpoint for each class interval
Multiply the midpoint by the frequency to get the sum of the products
Calculate the total frequency
Calculate the sample mean by dividing the sum of the products by the total frequency
Calculate the sample variance using the formula:

Sample variance = [(Σ(fx2)) / n] - (sample mean)2

Using the provided frequency distribution, the sample mean is approximately 86.9 and the sample variance is approximately 99.8.

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