Question

g. compute the standard deviation.
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Explanation:

To compute the standard deviation, we typically need a dataset. Since no dataset is provided here, we can't perform the calculation. However, I'll outline the general steps for calculating the population standard deviation (σ) or sample standard deviation (s) assuming we have a dataset \( x_1, x_2, \dots, x_n \):

For Population Standard Deviation (\(\boldsymbol{\sigma}\)):

Step 1: Calculate the mean (\(\boldsymbol{\mu}\))

The mean of the dataset is given by:

$$ \mu = \frac{\sum_{i = 1}^{n} x_i}{n} $$

where \( n \) is the number of data points.

Step 2: Calculate the squared deviations

For each data point \( x_i \), find the squared deviation from the mean: \( (x_i - \mu)^2 \).

Step 3: Calculate the variance (\(\boldsymbol{\sigma^2}\))

The population variance is the average of the squared deviations:

$$ \sigma^2 = \frac{\sum_{i = 1}^{n} (x_i - \mu)^2}{n} $$

Step 4: Calculate the standard deviation (\(\boldsymbol{\sigma}\))

Take the square root of the variance:

$$ \sigma = \sqrt{\frac{\sum_{i = 1}^{n} (x_i - \mu)^2}{n}} $$

For Sample Standard Deviation (\(\boldsymbol{s}\)):

Step 1: Calculate the sample mean (\(\boldsymbol{\bar{x}}\))

The sample mean is:

$$ \bar{x} = \frac{\sum_{i = 1}^{n} x_i}{n} $$

Step 2: Calculate the squared deviations

For each data point \( x_i \), find the squared deviation from the sample mean: \( (x_i - \bar{x})^2 \).

Step 3: Calculate the sample variance (\(\boldsymbol{s^2}\))

The sample variance uses \( n - 1 \) (degrees of freedom) in the denominator:

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

Step 4: Calculate the sample standard deviation (\(\boldsymbol{s}\))

Take the square root of the sample variance:

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

If you provide a dataset (e.g., a list of numbers), I can help you compute the standard deviation using these steps.

Answer:

To compute the standard deviation, we typically need a dataset. Since no dataset is provided here, we can't perform the calculation. However, I'll outline the general steps for calculating the population standard deviation (σ) or sample standard deviation (s) assuming we have a dataset \( x_1, x_2, \dots, x_n \):

For Population Standard Deviation (\(\boldsymbol{\sigma}\)):

Step 1: Calculate the mean (\(\boldsymbol{\mu}\))

The mean of the dataset is given by:

$$ \mu = \frac{\sum_{i = 1}^{n} x_i}{n} $$

where \( n \) is the number of data points.

Step 2: Calculate the squared deviations

For each data point \( x_i \), find the squared deviation from the mean: \( (x_i - \mu)^2 \).

Step 3: Calculate the variance (\(\boldsymbol{\sigma^2}\))

The population variance is the average of the squared deviations:

$$ \sigma^2 = \frac{\sum_{i = 1}^{n} (x_i - \mu)^2}{n} $$

Step 4: Calculate the standard deviation (\(\boldsymbol{\sigma}\))

Take the square root of the variance:

$$ \sigma = \sqrt{\frac{\sum_{i = 1}^{n} (x_i - \mu)^2}{n}} $$

For Sample Standard Deviation (\(\boldsymbol{s}\)):

Step 1: Calculate the sample mean (\(\boldsymbol{\bar{x}}\))

The sample mean is:

$$ \bar{x} = \frac{\sum_{i = 1}^{n} x_i}{n} $$

Step 2: Calculate the squared deviations

For each data point \( x_i \), find the squared deviation from the sample mean: \( (x_i - \bar{x})^2 \).

Step 3: Calculate the sample variance (\(\boldsymbol{s^2}\))

The sample variance uses \( n - 1 \) (degrees of freedom) in the denominator:

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

Step 4: Calculate the sample standard deviation (\(\boldsymbol{s}\))

Take the square root of the sample variance:

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

If you provide a dataset (e.g., a list of numbers), I can help you compute the standard deviation using these steps.