Question

find the standard deviation for the following group of data items. 12, 16, 16, 23 the standard deviation is approximately (round to two decimal places as needed )

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{12 + 16+16 + 23}{4}=\frac{67}{4}=16.75$

Step2: Calculate the squared differences

For \(12\): \((12 - 16.75)^{2}=(-4.75)^{2}=22.5625\)
For \(16\): \((16 - 16.75)^{2}=(-0.75)^{2}=0.5625\)
For \(16\): \((16 - 16.75)^{2}=(-0.75)^{2}=0.5625\)
For \(23\): \((23 - 16.75)^{2}=(6.25)^{2}=39.0625\)

Step3: Calculate the variance

The variance \(s^{2}=\frac{22.5625+0.5625 + 0.5625+39.0625}{4 - 1}=\frac{62.75}{3}\approx20.92\)

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{20.92}\approx4.57\)

Answer:

\(4.57\)