Question

the following data points are the number of points scored last basketball game by the 5 starting players on the dragons basketball team. 4, 21, 11, 6, 8. find the standard deviation of the data set. round your answer to the nearest hundredth.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{4 + 21+11+6+8}{5}=\frac{50}{5}=10$.

Step2: Calculate the squared - differences

$(4 - 10)^2=(-6)^2 = 36$, $(21 - 10)^2=11^2 = 121$, $(11 - 10)^2=1^2 = 1$, $(6 - 10)^2=(-4)^2 = 16$, $(8 - 10)^2=(-2)^2 = 4$.

Step3: Calculate the variance

The variance $s^{2}=\frac{36+121 + 1+16+4}{5}=\frac{178}{5}=35.6$.

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{35.6}\approx5.97$.

Answer:

$5.97$