Question

compute the standard deviation for the set of data. 13.3, 14.3, 15.3, 16.3, 17.3 a. √2 b. 2 c. √10 d. 4 please select the best answer from the choices provided a b c d

Explanation:

Step1: Find the mean ($\mu$)

The data set is \(13.3, 14.3, 15.3, 16.3, 17.3\). The number of data points \(n = 5\).
The mean \(\mu=\frac{13.3 + 14.3 + 15.3 + 16.3 + 17.3}{5}\)
\(=\frac{(13.3+17.3)+(14.3+16.3)+15.3}{5}=\frac{30.6+30.6+15.3}{5}=\frac{76.5}{5}=15.3\)

Step2: Calculate squared deviations

For each data point \(x_i\), calculate \((x_i - \mu)^2\):

• For \(x_1 = 13.3\): \((13.3 - 15.3)^2=(-2)^2 = 4\)
• For \(x_2 = 14.3\): \((14.3 - 15.3)^2=(-1)^2 = 1\)
• For \(x_3 = 15.3\): \((15.3 - 15.3)^2=0^2 = 0\)
• For \(x_4 = 16.3\): \((16.3 - 15.3)^2=(1)^2 = 1\)
• For \(x_5 = 17.3\): \((17.3 - 15.3)^2=(2)^2 = 4\)

Step3: Find the variance ($\sigma^2$)

Variance is the average of squared deviations.
\(\sigma^2=\frac{4 + 1+0 + 1+4}{5}=\frac{10}{5} = 2\)

Step4: Find the standard deviation ($\sigma$)

Standard deviation is the square root of variance.
\(\sigma=\sqrt{\sigma^2}=\sqrt{2}\)

Answer:

A. \(\sqrt{2}\)