A researcher has collected the following sample data.   351232The variance isGroup of answer choices

Break Down the Problem

1. Identify the provided sample data: 351232.
2. Determine that we need to calculate the variance of this sample data set.

Relevant Concepts

3. The formula for calculating sample variance $s^2$ is given by: $s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2$ where:
   • $n$ = number of observations
   • $x_i$ = each observation
   • $\bar{x}$ = sample mean

Analysis and Detail

4. Calculate the sample mean $\bar{x}$:

   • Sample Data: 3, 5, 1, 2, 3, 2
   • Sum of Data: $3 + 5 + 1 + 2 + 3 + 2 = 16$
   • Number of observations: $n = 6$
   • Sample Mean: $\bar{x} = \frac{16}{6} \approx 2.67$

5. Calculate each deviation from the mean and square it:

   • $(3 - 2.67)^2 = 0.11$
   • $(5 - 2.67)^2 = 5.44$
   • $(1 - 2.67)^2 = 2.78$
   • $(2 - 2.67)^2 = 0.44$
   • $(3 - 2.67)^2 = 0.11$
   • $(2 - 2.67)^2 = 0.44$

6. Sum of squared deviations: $0.11 + 5.44 + 2.78 + 0.44 + 0.11 + 0.44 = 9.32$

7. Calculate the sample variance: $s^2 = \frac{9.32}{6-1} = \frac{9.32}{5} \approx 1.864$

Verify and Summarize

8. The calculations have been verified, and all steps have been clearly followed.

Final Answer

The variance of the sample data is approximately $1.864$.