This page continues the step-by-step standard deviation calculation tutorial by presenting two more examples, further reinforcing the concept and providing additional practice for students.

Example 1: The first example uses the dataset: 15, 18, 14, 17, 16, 19.

1. Calculate the mean: $15 + 18 + 14 + 17 + 16 + 19$ / 6 = 16.5
2. The page then demonstrates the calculation of the standard deviation using a slightly different formula:

S = √((Σx² - (Σx)² / n) / $n - 1$)

Where:

• Σx² is the sum of squared values
• (Σx)² is the square of the sum of values
• n is the number of values

Highlight: The calculated standard deviation for this example is 1.87.

Example 2: The second example uses the dataset: 54, 45, 51, 50, 48, 53, 49.

1. Calculate the mean: $54 + 45 + 51 + 50 + 48 + 53 + 49$ / 7 = 50

The page begins to show the calculation process for this example using the same formula as in Example 1, but does not provide the final result.

Vocabulary: Σx² (sum of squares) - The sum of all values in a dataset after each value has been squared.

These additional examples help reinforce the concept of standard deviation calculation and provide students with more practice in applying the formulas to different datasets. The page effectively demonstrates the versatility of the standard deviation formula and how it can be applied to various sets of numbers.

This page introduces the concept of standard deviation and provides a detailed example of how to calculate it. The standard deviation is a measure of variability in a dataset that indicates how spread out the values are from the mean.

Definition: Standard deviation (S.D.) is a statistical measure that quantifies the amount of variation or dispersion of a set of data values.

The page presents the formula for standard deviation:

S.D = √$Σ(x - x̄)² / (n - 1)$

Where:

• x represents each value in the dataset
• x̄ is the mean of the dataset
• n is the number of values

Example: The page walks through a detailed example of how to find standard deviation with examples using the dataset: 30, 41, 48, 29.

The calculation process is broken down into several steps:

1. Calculate the mean: $30 + 41 + 48 + 29$ / 4 = 37
2. Find the deviation of each value from the mean
3. Square each deviation
4. Sum the squared deviations
5. Divide by $n-1$
6. Take the square root of the result

Highlight: The final calculated standard deviation for this example is 9.13.

This page provides a thorough explanation of the standard deviation calculation process, making it an excellent resource for students learning this important statistical concept.