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A ALEKS Shimmareeyau Williams - Knowledge Checkhttps://www-awu.aleks.com/alekscgi/x/Islexe/1o_u-IgNsikr7j8P3JH-1JxL2PxI5SYVRXF19F_OAHM6RX26Tns_nmodtyeSmOWES...&EInitial Knowledge CheckQuestion 17The 6 participants in a 200-meter dash had the following finishing times in seconds).aA31, 29, 29, 24, 24, 31Send data to calculator+Assuming that these times constitute an entire population, find the standard deviation of the population. Round your answer to two decimal

A ALEKS Shimmareeyau Williams Knowledge CheckhttpswwwawualekscomalekscgixIslexe1ouIgNsikr7j8P3JH1JxL2PxI5SYVRXF19FOAHM6RX26TnsnmodtyeSmOWESampEInitial Knowledge class=

Sagot :

Solution:

The standard deviation is expressed as

where

[tex]\begin{gathered} x_i\Rightarrow sample\text{ values} \\ \mu\implies mean \\ N\implies number\text{ of observation} \\ \sigma\Rightarrow standard\text{ deviation} \end{gathered}[/tex]

Given the sample data below:

[tex]31,\text{ 29, 29, 24, 24, 31}[/tex]

Step 1: Evaluate the mean.

The mean is evaluated as

[tex]\begin{gathered} \mu=\frac{31+29+29+24+24+31}{6} \\ =\frac{168}{6} \\ \Rightarrow\mu=28 \end{gathered}[/tex]

Step 2: Evaluate the standard deviation.

Thus, we have

[tex]\begin{gathered} \sigma=\sqrt{\frac{(31-28)^2+(29-28)^2+(29-28)^2+(24-28)^2+(24-28)^2+(31-28)^2}{6}} \\ =\sqrt{\frac{52}{6}} \\ =2.943920289 \\ \Rightarrow\sigma\approx2.94\text{ \lparen2 decimal places\rparen} \end{gathered}[/tex]

Hence, the standard deviation of the population, to two decimal places, is

[tex]2.94[/tex]

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