Using the example from table 6.4 , calculate the mean numbers and standard deviation of the pousing the data in table 6.3 Is of the study.may be 10 m³ because of the size of the study species; in a rockyy. For instance, when determining Treeal zone, the quadrat may only be 0.25 m² because much smaller organisms are being studied.Quadrat surveys are useful in rocky intertidal areas because the majority of organisms located thereare slow-moving, attached to the substrate or plants.Scientists use a method of random sampling to determine where to place the quadrat whenconducting a survey. This prevents any bias affecting the data. The counts from each quadrat are thenaveraged to reach an approximate number for the entire area.Scientists were conducting a quadrat survey on a rocky shore in Vancouver, BC, Canada. They werespecifically investigating the abundance of leather stars (Dermasterias imbricate) and the Pacificblue mussel (Mytilus trossulus) along the shore. Square quadrats of 1 m² were used to measure theabundance in ten randomly selected locations (see Table 6.3).sample areanumber of leather 3stars in 1 m²number of mussels 20in 1 m-21549309847Table 6.3. Results of 1 m² sample area calculations.5412617100712488110921610932 0•Often scientists include standard deviation in their results when they analyse their data. Standarddeviations tell you how spread out the numbers in a data set are. The smaller the standard deviation,within a community. The equation for standard deviation is:the closer the numbers are to the mean. This can tell you, for example, how variable a population isThese symbols all relate to the different steps you need to complete to find the standard deviation.given in Table 6.3 is calculated as shown below.This equation can be broken down into stages. The standard deviation (S) for the leather star dataCalculate the mean value (F) for the leather star population:sample areanumber ofleather starsin 1 m²(x-x)²(x-x). So for quadrat 1: (3 - 7.1)² = 16.8.Then for each quadrat, subtract the mean (x) from its number (x) and square the result, giving you:Table 6.4 shows the results of this step for all 10 quadrats.I310215X = (3+15+0+8+4+17+12+1+2+9)1030S= Σ(x-x)²V #-14816.8 62.4 50.4 0.8549.661771298.0 24.08= 7,11Chapter 6: The ocean floor and the co92109meanTable 6.4. Working out the mean values for the leather stars.The next step is to calculate E(x-x) by adding all of the (x-) values. So, E(x - x)² = 328.8111Then, divide your value for E(x-x)2 by (n-1), where is the number of values you have(10, in this case). This should provide you with a value of 36.53.Finally, take the square root of your calculated value.• Using this equation, your standard deviation should be 6.04.7.137.2 26.0 3.61 32.9I a Calculate the mean numbers per m² for the mussels, using the data in Table 6.3.b Calculate the standard deviation for the population of mussels.2 Based on your knowledge of rocky intertidal zone communities, predict which quadrats wereplaced in the lower intertidal zone and which were placed in the upper intertidal zone.371572017-1171

The data on the 1 m2 sample area calculation are sample no of leather star in 1 m2no of mussels in…

Answered: Ut the study. ance, when determining…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Using the example from table 6.4 , calculate the mean numbers and standard deviation of the pousing the data in table 6.3

Is of the study.
may be 10 m³ because of the size of the study species; in a rocky
y. For instance, when determining Tree
al zone, the quadrat may only be 0.25 m² because much smaller organisms are being studied.
Quadrat surveys are useful in rocky intertidal areas because the majority of organisms located there
are slow-moving, attached to the substrate or plants.
Scientists use a method of random sampling to determine where to place the quadrat when
conducting a survey. This prevents any bias affecting the data. The counts from each quadrat are then
averaged to reach an approximate number for the entire area.
Scientists were conducting a quadrat survey on a rocky shore in Vancouver, BC, Canada. They were
specifically investigating the abundance of leather stars (Dermasterias imbricate) and the Pacific
blue mussel (Mytilus trossulus) along the shore. Square quadrats of 1 m² were used to measure the
abundance in ten randomly selected locations (see Table 6.3).
sample area
number of leather 3
stars in 1 m²
number of mussels 20
in 1 m-
2
15
49
3
0
9
8
47
Table 6.3. Results of 1 m² sample area calculations.
5
4
12
6
17
100
7
12
48
8
1
10
9
2
16
10
9
32

0
•
Often scientists include standard deviation in their results when they analyse their data. Standard
deviations tell you how spread out the numbers in a data set are. The smaller the standard deviation,
within a community. The equation for standard deviation is:
the closer the numbers are to the mean. This can tell you, for example, how variable a population is
These symbols all relate to the different steps you need to complete to find the standard deviation.
given in Table 6.3 is calculated as shown below.
This equation can be broken down into stages. The standard deviation (S) for the leather star data
Calculate the mean value (F) for the leather star population:
sample area
number of
leather stars
in 1 m²
(x-x)²
(x-x). So for quadrat 1: (3 - 7.1)² = 16.8.
Then for each quadrat, subtract the mean (x) from its number (x) and square the result, giving you:
Table 6.4 shows the results of this step for all 10 quadrats.
I
3
10
2
15
X = (3+15+0+8+4+17+12+1+2+9)
10
3
0
S= Σ(x-x)²
V #-1
4
8
16.8 62.4 50.4 0.8
5
4
9.6
6
17
7
12
98.0 24.0
8
= 7,1
1
Chapter 6: The ocean floor and the co
9
2
10
9
mean
Table 6.4. Working out the mean values for the leather stars.
The next step is to calculate E(x-x) by adding all of the (x-) values. So, E(x - x)² = 328.81
11
Then, divide your value for E(x-x)2 by (n-1), where is the number of values you have
(10, in this case). This should provide you with a value of 36.53.
Finally, take the square root of your calculated value.
• Using this equation, your standard deviation should be 6.04.
7.1
37.2 26.0 3.61 32.9
I a Calculate the mean numbers per m² for the mussels, using the data in Table 6.3.
b Calculate the standard deviation for the population of mussels.
2 Based on your knowledge of rocky intertidal zone communities, predict which quadrats were
placed in the lower intertidal zone and which were placed in the upper intertidal zone.
37157
2017-1
1
71

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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