Questions: Find the standard deviation, σ, of the data. 84,98,70,76,88,76 x̄=82 Variance (σ^2)=85.3 σ=[?] Round to the nearest tenth.

Transcript text: Find the standard deviation, $\sigma$, of the data. \[ \begin{array}{c} 84,98,70,76,88,76 \\ \bar{x}=82 \\ \text { Variance }\left(\sigma^{2}\right)=85.3 \\ \sigma=[?] \end{array} \] Round to the nearest tenth.

Solution

Solution Steps

Step 1: Identify the given values

The problem provides the following values:

Data points: $ 84, 98, 70, 76, 88, 76 $
Mean ($ \bar{x} $): $ 82 $
Variance ($ \sigma^2 $): $ 85.3 $

Step 2: Recall the relationship between variance and standard deviation

The standard deviation ($ \sigma $) is the square root of the variance ($ \sigma^2 $). Mathematically, this is expressed as: \[ \sigma = \sqrt{\sigma^2} \]

Step 3: Calculate the standard deviation

Substitute the given variance into the formula: \[ \sigma = \sqrt{85.3} \] \[ \sigma \approx 9.236 \]

Step 4: Round the standard deviation to the nearest tenth

Rounding $ 9.236 $ to the nearest tenth gives: \[ \sigma \approx 9.2 \]