Answer :
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.
[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 data
where
[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 more
- Learn more about standard deviation https://brainly.com/question/11344811
Answer details
Grade: 9
Subject: mathematics
Chapter: standard deviation
Keywords: standard deviation
The standard deviation of the water depth is [tex]\boxed{1.44}[/tex].
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.
[tex]\boxed{X \sim\text{Uniform} \left( {a,b} \right)}[/tex]
The variance can be obtained as,
[tex]\boxed{{\text{Variance}} = \frac{1}{{12}}{{\left( {b - a} \right)}^2}}[/tex]
Calculation:
The standard deviation is square root of variance.
The depth of water is in between the data set [tex]2 \text{ m}[/tex] to [tex]7 \text{ m}[/tex].
The depth of water follows uniform distribution.
The variance of the depth of water can be obtained as,
[tex]\begin{aligned} {\text{variance}} &= \frac{1}{{12}}{\left( {7 - 2} \right)^2} \\ &= \frac{{{5^2}}}{{12}} \\ &= \frac{{25}}{{12}} \\ \end{aligned}[/tex]
The standard deviation can be obtained as,
[tex]\begin{aligned} {\text{standard deviation}} &= \sqrt {\frac{{25}}{{12}}} \\ &= 1.44 \\ \end{aligned}[/tex]
The standard deviation of the water depth is [tex]\boxed{1.44}[/tex].
Learn more:
1. Learn more about normal distribution https://brainly.com/question/12698949
2. Learn more about standard normal distribution https://brainly.com/question/13006989
3. Learn more about confidence interval of mean https://brainly.com/question/12986589
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.