Questions: Find the standard deviation, σ, of the data. 15,21,46,49,31,24 x̄=31 Variance (σ^2)=159 σ=[?] Round to the nearest tenth

Transcript text: Find the standard deviation, $\sigma$, of the data. \[ \begin{array}{c} 15,21,46,49,31,24 \\ \bar{x}=31 \\ \text { Variance }\left(\sigma^{2}\right)=159 \\ \sigma=[?] \end{array} \] Round to the nearest tenth

Solution

Solution Steps

Step 1: Given Data

The dataset provided is: \[ \{15, 21, 46, 49, 31, 24\} \] The mean ($\bar{x}$) of the dataset is given as: \[ \bar{x} = 31 \] The variance ($\sigma^2$) is given as: \[ \sigma^2 = 159 \]

Step 2: Calculate Standard Deviation

The standard deviation ($\sigma$) is calculated using the formula: \[ \sigma = \sqrt{\sigma^2} \] Substituting the value of variance: \[ \sigma = \sqrt{159} \] Calculating this gives: \[ \sigma \approx 12.588 \] Rounding to the nearest tenth, we have: \[ \sigma \approx 12.6 \]