Mathematics, 23.07.2019 17:00 kylee76

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?

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Answer from: Molly05

The standard deviation of the water depth is 3.53

Further 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.

$standard deviation = \sqrt{\frac{\Sigma^n_{i=1} {x_i - x-^{2} } \, dx }{n-1} }$

where

x_i = value data

= number of data

= mean of the data

where

x_i = 2 m

x_2 = 7 m

$x- = \frac{2+7}{2} = 4.5$

$standard deviation = \sqrt{\frac{(2-4.5)^{2}+ (7-2.5)^{2} }{2-1} } \\ standard deviation = 3.53$

Learn moreLearn more about standard deviation Answer details

Grade: 9

Subject: mathematics

Chapter: standard deviation

Keywords: standard deviation

Answer from: lreese

The standard deviation of the water depth is $\boxed{1.44}$ .

Further Explanation:

The standard deviation is a measure of deviation of data values from mean. And it also measure the spreadness of the data values.

More the standard deviation more the spreadness and less the standard deviation less will be the spreadness.

The random variable X follows uniform distribution in interval a to b.

$\boxed{X \sim\text{Uniform} \left( {a,b} \right)}$

The variance can be obtained as,

$\boxed{{\text{Variance}} = \frac{1}{{12}}{{\left( {b - a} \right)}^2}}$

Calculation:

The standard deviation is square root of variance.

The depth of water is in between the data set $2 \text{ m}$ to $7 \text{ m}$ .

The depth of water follows uniform distribution.

The variance of the depth of water can be obtained as,

$\begin{aligned} {\text{variance}} &= \frac{1}{{12}}{\left( {7 - 2} \right)^2} \\ &= \frac{{{5^2}}}{{12}} \\ &= \frac{{25}}{{12}} \\ \end{aligned}$

The standard deviation can be obtained as,

$\begin{aligned} {\text{standard deviation}} &= \sqrt {\frac{{25}}{{12}}} \\ &= 1.44 \\ \end{aligned}$

The standard deviation of the water depth is $\boxed{1.44}$ .

Learn more:

1. Learn more about normal distribution

2. Learn more about standard normal distribution

3. Learn more about confidence interval of mean

Answer details:

Grade: College

Subject: Statistics

Chapter: Confidence Interval

Keywords: Z-score, Z-value, binomial distribution, standard normal distribution, standard deviation, criminologist, test, measure, mean, normal distribution, percentile, percentage, proportion, depth, water depth, conducting experiment, marine, biologist, selects, uniformly distributed, uniform distribution, between 2 m and 7 m.

Answer from: Quest

It’s hard to understand what you put.. can you show a picture ?

Answer from: Quest

step-by-step explanation: