Question

standard deviations for two observations 1 and 4 is ?​

Answer 1

Answer:

For the normal distribution, this accounts for 68.27 percent of the set; while two standard deviations from the mean (medium and dark blue) account for 95.45 percent; three standard deviations (light, medium, and dark blue) account for 99.73 percent; and four standard deviations account for 99.994 percent.

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Answer 2

Answer:

The standard deviation for two observations is $1.5$

Step-by-step explanation:

Given:

observations are 1 and 4

To find:

The standard deviation of the given two observations

Solution:

First, we find out the mean of the given two observations

Mean,$\bar{x}=\frac{1+4}{2}\\=\frac{5}{2}$

The formula for Standard deviation :

$\text { S.D }=\sqrt{\frac{\sum\left(\mathrm{x}_{\mathrm{i}}-\bar{x}\right)^{2}}{n}}$

$S . D=\sqrt{\frac{\left(x_{1}-\bar{x}\right)^{2}+\left(x_{1}-\bar{x}\right)^{2}}{2}}$

$S . D=\sqrt{\frac{\left(1-\frac{5}{2}\right)^{2}+\left(4-\frac{5}{2}\right)^{2}}{2}}$

$S . D=\sqrt{\frac{\left(\frac{2-5}{2}\right)^{2}+\left(\frac{8-5}{2}\right)^{2}}{2}}$

$\begin{aligned}&S . D=\sqrt{\frac{\left(\frac{-3}{2}\right)^{2}+\left(\frac{3}{2}\right)^{2}}{2}} \\&S . D=\sqrt{\frac{\frac{9}{4}+\frac{9}{4}}{2}} \\&S . D=\sqrt{\frac{\frac{18}{4}}{2}} \\&\text { S.D }=\sqrt{\frac{\frac{9}{2}}{2}} \\&\text { S.D }=\sqrt{\frac{9}{4}}\end{aligned}$

$S.D=\frac{3}{2} \\\\=1.5$