Question

from the following set of data, the standard deviation is data set: {3, 2, 14, 4} note: round your answer to the nearest tenth.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{3 + 2+1 + 4}{4}=\frac{10}{4} = 2.5$

Step2: Calculate the squared - differences

$(3 - 2.5)^2=0.25$, $(2 - 2.5)^2 = 0.25$, $(1 - 2.5)^2=2.25$, $(4 - 2.5)^2 = 2.25$

Step3: Calculate the variance

The variance $s^{2}=\frac{0.25+0.25 + 2.25+2.25}{4}=\frac{5}{4}=1.25$

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{1.25}\approx1.1$

Answer:

$1.1$