To solve the questions about Group A and Group B data, let's calculate each value as follows:

Given Data:

Group A: 3, 5, 7, 5, 6, 3, 1, 2
Group B: 5, 7, 3, 6, 7, 8

Let's go through each question step-by-step.

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1. What is $n$ for Group A?

• Answer: $n$ for Group A is the number of data points. Group A has 8 values, so $n = 8$.

2. What is $n$ for Group B?

• Answer: $n$ for Group B is the number of data points. Group B has 6 values, so $n = 6$.

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3. What is $\bar{x}$ (mean) for Group A?

To find the mean $\bar{x}$, use the formula: $\bar{x} = \frac{\sum x}{n}$ For Group A: $\bar{x}_A = \frac{3 + 5 + 7 + 5 + 6 + 3 + 1 + 2}{8} = \frac{32}{8} = 4$

• Answer: $\bar{x}_A = 4$.

4. What is $\bar{x}$ (mean) for Group B?

For Group B: $\bar{x}_B = \frac{5 + 7 + 3 + 6 + 7 + 8}{6} = \frac{36}{6} = 6$

• Answer: $\bar{x}_B = 6$.

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5. What is $s^2$ (variance) for Group A?

To calculate the variance $s^2$, use the formula: $s^2 = \frac{\sum (x - \bar{x})^2}{n - 1}$ For Group A:

1. Find $\bar{x}_A = 4$.
2. Calculate $(x - \bar{x}_A)^2$ for each value in Group A:
   • $(3 - 4)^2 = 1$
   • $(5 - 4)^2 = 1$
   • $(7 - 4)^2 = 9$
   • $(5 - 4)^2 = 1$
   • $(6 - 4)^2 = 4$
   • $(3 - 4)^2 = 1$
   • $(1 - 4)^2 = 9$
   • $(2 - 4)^2 = 4$
3. Sum of squares: $1 + 1 + 9 + 1 + 4 + 1 + 9 + 4 = 30$.
4. Divide by $n - 1$: $s^2 = \frac{30}{8 - 1} = \frac{30}{7} \approx 4.2857$.

• Answer: $s^2 \approx 4.2857$.

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Let me know if you would like any additional steps explained in detail.

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Related Questions:

1. What is the standard deviation $s$ for Group A?
2. What is the standard deviation $s$ for Group B?
3. What is the median of Group A?
4. What is the median of Group B?
5. What is the range of values for Group A and Group B?

Tip:

To ensure accuracy, always double-check values when calculating variance by hand, as each squared deviation is essential for the correct result.