Question

the following data points are the number of words that 5 students found in a word search puzzle. 18,16,15,15,16. find the standard deviation of the data set. round your answer to the nearest hundredth.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{18 + 16+15+15+16}{5}=\frac{80}{5}=16$.

Step2: Calculate the squared - differences

$(18 - 16)^2=4$, $(16 - 16)^2 = 0$, $(15 - 16)^2=1$, $(15 - 16)^2=1$, $(16 - 16)^2 = 0$.

Step3: Calculate the variance

The variance $s^{2}=\frac{4+0 + 1+1+0}{5}=\frac{6}{5}=1.2$.

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{1.2}\approx1.0954\approx1.10$.

Answer:

$1.10$