To calculate the composite standard deviation (also called the pooled standard deviation) for two groups, the formula is:

$s_{\text{pooled}} = \sqrt{\frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}}$

Where:

• $s_1$ and $s_2$ are the standard deviations of Group 1 and Group 2, respectively.
• $n_1$ and $n_2$ are the number of observations in Group 1 and Group 2, respectively.

Given dataTo calculate the composite standard deviation (also called the pooled standard deviation) for two groups, the formula is:

$s_{\text{pooled}} = \sqrt{\frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}}$

Where:

• $s_1$ and $s_2$ are the standard deviations of Group 1 and Group 2, respectively.
• $n_1$ and $n_2$ are the number of observations in Group 1 and Group 2, respectively.

Given

• Group 1: $s_1 = 1.25$, $n_1 = 25$
• Group 2: $s_2 = 2.2$, $n_2 = 45$

Now, let’s compute the pooled standard deviation.

$s_{\text{pooled}} = \sqrt{\frac{(25 - 1)(1.25)^2 + (45 - 1)(2.2)^2}{25 + 45 - 2}}$

Let’s calculate this step-by-step.The composite (pooled) standard deviation for the two groups is approximately 1.92.

Would you like further details on the calculation or have any other questions? Here are five related questions to deepen your understanding:

1. How does the sample size affect the pooled standard deviation?
2. What is the significance of using pooled standard deviation in hypothesis testing?
3. How does pooled standard deviation differ from weighted standard deviation?
4. Can we use the pooled standard deviation if the variances of the two groups differ significantly?
5. How would you interpret the pooled standard deviation in the context of your data?

Tip: Pooled standard deviation is most useful when the sample sizes and variances of the two groups are not drastically different.