Question

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Explanation:

Identify the dataset and objectives

We have a sample of \(n = 6\) red blood cell counts:

$$ 51, 55, 48, 49, 54, 49 $$

Using Descriptive Statistics, we will calculate the sample mean and sample standard deviation.

Calculate the sample mean

The sample mean \(\bar{x}\) is calculated as:

$$ \bar{x} = \frac{\sum x_i}{n} $$

Summing the values:

$$ \sum x_i = 51 + 55 + 48 + 49 + 54 + 49 = 306 $$

Dividing by \(n = 6\):

$$ \bar{x} = \frac{306}{6} = 51 $$

Calculate the sample variance

The sample variance \(s^2\) is calculated as:

$$ s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1} $$

First, find the squared deviations from the mean \(\bar{x} = 51\):

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Summing these squared deviations:

$$ \sum (x_i - \bar{x})^2 = 0 + 16 + 9 + 4 + 9 + 4 = 42 $$

Dividing by \(n - 1 = 5\):

$$ s^2 = \frac{42}{5} = 8.4 $$

Calculate the sample standard deviation

The sample standard deviation \(s\) is the square root of the sample variance:

$$ s = \sqrt{8.4} \approx 2.898 $$

Answer:

For the red blood cell counts \(51, 55, 48, 49, 54, 49\):

• Sample Mean (\(\bar{x}\)): \(51 \times 10^5\) cells per microliter
• Sample Standard Deviation (\(s\)): \(\approx 2.90 \times 10^5\) cells per microliter (or \(\sqrt{8.4} \approx 2.898\))