Question

tonys soccer team played 6 games. they scored: 8 goals 6 goals 8 goals 6 goals 1 goal 7 goals what was the standard deviation of the numbers of goals tonys team scored? if the answer is a decimal, round it to the nearest tenth. standard deviation (σ): goals

Explanation:

Step1: Calculate the mean

The data set is \(x = \{8,6,8,6,1,7\}\).
The mean \(\bar{x}=\frac{8 + 6+8+6 + 1+7}{6}=\frac{36}{6}=6\)

Step2: Calculate the squared differences from the mean

\((8 - 6)^2=4\), \((6 - 6)^2 = 0\), \((8 - 6)^2=4\), \((6 - 6)^2=0\), \((1 - 6)^2=25\), \((7 - 6)^2 = 1\)

Step3: Calculate the variance

The variance \(\sigma^{2}=\frac{4+0 + 4+0+25+1}{6}=\frac{34}{6}\approx5.67\)

Step4: Calculate the standard deviation

The standard deviation \(\sigma=\sqrt{\frac{34}{6}}\approx2.4\)

Answer:

\(2.4\)