Question

Determine the age and sample standard deviation for each of the due sets. For the sample standard deviation round each answer to one more decimal place than that used for the observation.

Amphibian Embroyes. In a study of the effects of radiation on amphibian embryos titled "Shedding Light on Ultraviolet Radiation and Amphibian Embryos" ( Bio Science, Vol. 53. No. 6. pp. 551561) L. Licht recorded the time it took for a sample of seven different species of frogs and toads' eggs to hatch. The following table shows the times to hatch, in days

$6,7,11,6,5,5,11$

Short answer

Range of the data $=6$

Standard deviation of the data$=2.6$

Step-by-step solution

Step 1. Given information.  

We have given data:$6,7,11,6,5,5,11$

Step 2. To find range of the data.  

$$\begin{gathered} Range=Max.val-Minval. \\ Range=11-5 \\ Range=6 \end{gathered}$$

Step 3. To find mean of the data 

$$\begin{gathered} Mean=\frac{Sumofallobservation}{Numberofobservation} \\ =\frac{6+7+11+6+5+5+11}{7} \\ =\frac{51}{7} \\ =7.285 \end{gathered}$$

Step 4. To find standard deviation of the data. 

$x$	$x-\overline{x}$	${\left(x-\overline{x}\right)}^2$
$$\begin{gathered} 6 \\ 7 \\ 11 \\ 6 \\ 5 \\ 5 \\ 11 \end{gathered}$$	$$\begin{gathered} -1.3 \\ -0.3 \\ 3.7 \\ -1.3 \\ -2.3 \\ -2.3 \\ 3.7 \end{gathered}$$	$$\begin{gathered} 1.69 \\ 0.09 \\ 13.69 \\ 1.69 \\ 5.29 \\ 5.29 \\ 13.69 \end{gathered}$$

$$\begin{gathered} S\tan darddeviation=\sqrt{\frac{{\left(x-\overline{x}\right)}^2}{n-1}} \\ =\sqrt{\frac{41.43}{6}} \\ =2.62774 \\ =2.6 \end{gathered}$$