Question

find the standard deviation for the following group of data items. 16, 19, 19, 25 the standard deviation is approximately (round to two decimal places as needed.)

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{16 + 19+19+25}{4}=\frac{79}{4}=19.75$

Step2: Calculate the squared differences

$(16 - 19.75)^2=(- 3.75)^2 = 14.0625$
$(19 - 19.75)^2=(-0.75)^2=0.5625$
$(19 - 19.75)^2=(-0.75)^2=0.5625$
$(25 - 19.75)^2=(5.25)^2 = 27.5625$

Step3: Calculate the variance

The variance $s^{2}=\frac{14.0625+0.5625 + 0.5625+27.5625}{4 - 1}=\frac{42.75}{3}=14.25$

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{14.25}\approx3.77$

Answer:

$3.77$