Question

ms. johnson uses a statistics program to analyze all the data collected by her students during a lab experiment about acceleration due to gravity. the program reports \\(\bar{x}=31.5\\) and \\(sigma = 2.5\\). what is the variance of the data? round to the nearest tenth. \\(\circ\\) 1.6 \\(\circ\\) 2.5 \\(\circ\\) 5.6 \\(\circ\\) 6.3

Explanation:

Step1: Recall the relationship between standard deviation and variance

The variance (\(\sigma^2\)) is the square of the standard deviation (\(\sigma\)). So we use the formula \(\sigma^2=\sigma\times\sigma\).

Step2: Substitute the given standard deviation

We know that \(\sigma = 2.5\). So we calculate \(\sigma^2=(2.5)^2\).

Step3: Calculate the square

\((2.5)^2 = 2.5\times2.5=6.25\).

Step4: Round to the nearest tenth

\(6.25\) rounded to the nearest tenth is \(6.3\).

Answer:

6.3