Hello, the answer to point d is as follows. However, I am not sure how we got the exact values for each standard deviation. please explainBy using mean() in R, the mean= 206.45, and st() the standard deviation = 66.42.Percentage lies within 3 standard [7.19, 405.71] is 100%Percentage lies within 2 standard deviation [73.61, 339.29] is 95%Percentage lies within 1 standard deviation [140.03, 272.87] is 71.67% thank you. Exercise 4: (Empirical rule)1. Recall the empirical Rule.2. One study, published in 1972 by R. Risebrough, (Proceedings of the 6th Berkeley Symposium onMathematics and Statistics, VI, University of California Press, pp. 443–463). In that study, 60 Anacapapelican eggs were collected and measured for their shell thickness, in millimeters (mm), andconcentration of PCBS, in parts per million (ppm). The PCB concentrations are presented in thefollowing table:139166175 260 2041383163964621817322014721621617724629618889198122250256261132212171164199214177205208320191305230204143175119216185236356289324109265193 20321415022923614423287237a. Draw the relative frequency histogram using R.b. Is it reasonable to apply the Empirical rule to estimate the percentages of observations that lie withinone, two, and three standard deviations to either side of the mean?c. Use the empirical rule to estimate the percentages of observations that lie within one, two, and threestandard deviations to either side of the mean.d. Use the data to obtain the exact percentages of observations that lie within one, two, and threestandard deviations to either side of the mean.e. Compare your answers in parts (b) and (c).

Answered: Hello, the answer to point d is as…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

Hello,

the answer to point d is as follows. However, I am not sure how we got the exact values for each standard deviation. please explain

By using mean() in R, the mean= 206.45, and st() the standard deviation = 66.42.

Percentage lies within 3 standard [7.19, 405.71] is 100%
Percentage lies within 2 standard deviation [73.61, 339.29] is 95%
Percentage lies within 1 standard deviation [140.03, 272.87] is 71.67%

thank you.

Exercise 4: (Empirical rule)
1. Recall the empirical Rule.
2. One study, published in 1972 by R. Risebrough, (Proceedings of the 6th Berkeley Symposium on
Mathematics and Statistics, VI, University of California Press, pp. 443–463). In that study, 60 Anacapa
pelican eggs were collected and measured for their shell thickness, in millimeters (mm), and
concentration of PCBS, in parts per million (ppm). The PCB concentrations are presented in the
following table:
139
166
175 260 204
138
316
396
46
218
173
220
147
216
216
177
246
296
188
89
198
122
250
256
261
132
212
171
164
199
214
177
205
208
320
191
305
230
204
143
175
119
216
185
236
356
289
324
109
265
193 203
214
150
229
236
144
232
87
237
a. Draw the relative frequency histogram using R.
b. Is it reasonable to apply the Empirical rule to estimate the percentages of observations that lie within
one, two, and three standard deviations to either side of the mean?
c. Use the empirical rule to estimate the percentages of observations that lie within one, two, and three
standard deviations to either side of the mean.
d. Use the data to obtain the exact percentages of observations that lie within one, two, and three
standard deviations to either side of the mean.
e. Compare your answers in parts (b) and (c).

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 + ...

Expert Solution