While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. what is the standard deviation of the water depth?

Accepted Solution

The standard deviation of the water depth is 3.53Further explanation The standard deviation is a measure that is used to quantify the amount of variation or dispersion of a set of data values. The standard deviation is a measure of how spread out numbers are.  Its symbol is σ (the greek letter sigma)  The formula is the square root of the Variance. The variance is defined as the average of the squared differences from the mean.There are steps to calculate the variance: Work out the Mean (the simple average of the numbers) Then for each number: subtract the Mean and square the result (the squared difference). Then work out the average of those squared differences. A low standard deviation means that most of the numbers are close to the average. Whereas the high standard deviation means that the numbers are more spread out.[tex]standard deviation  = \sqrt{\frac{\Sigma^n_{i=1} {x_i - x-^{2} } \, dx }{n-1} }[/tex]where[tex]x_i[/tex] = value data[tex]n[/tex]  = number of data[tex]x-[/tex] = mean of the datawhere[tex]x_i[/tex] = 2 m[tex]x_2[/tex] = 7 m[tex]x- = \frac{2+7}{2}  = 4.5[/tex][tex]standard deviation = \sqrt{\frac{(2-4.5)^{2}+ (7-2.5)^{2}  }{2-1} }  \\ standard deviation = 3.53 [/tex]Learn moreLearn more about standard deviation detailsGrade:  9Subject:  mathematicsChapter:  standard deviation Keywords:    standard deviation