Question

Find the standard deviation, s, of sample data summarized in the frequency distribution table?

Answer 1

The calculation for the standard deviation (s) of the dataset is a fundamental statistical measure of dispersion.

Step-by-step explanation:

To compute the standard deviation from a frequency distribution table, begin by calculating the mean of the dataset using the formula:

Mean =
`(\sum(f \cdot x))/(N) \]`

Where \(f\) represents the frequency of each data point, x is the corresponding value, and N is the total number of observations. Then, compute the variance using the formula:

Variance =
`\frac{\sum(f \cdot (x - \text{Mean})^2)}{N} \]`

Finally, the standard deviation, denoted as s, is the square root of the variance:

s =
`\sqrt{\text{Variance}} \]`

This process accounts for the frequencies associated with each value, allowing for a more accurate representation of the spread of the dataset. The standard deviation provides insight into how much the individual data points deviate from the mean. It measures the dispersion or variability within the dataset; a larger standard deviation indicates greater variability among the data points, while a smaller standard deviation suggests that the values are closer to the mean.

Here is complete question;

"Given the frequency distribution table representing sample data, determine the standard deviation, denoted as 's,' to measure the dispersion or variability within the dataset. Utilize the provided frequency values and corresponding data points to compute the standard deviation, which is a crucial statistical metric for understanding the spread of values in a sample."