Answered: The histogram shows the distribution of hurricanes that have hit a country from 1851 through 2015, where 1 is the weakest level and 5 is the strongest level.…

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

The histogram shows the distribution of hurricanes that have hit a country from 1851 through 2015, where 1 is the weakest level and 5 is the strongest level.

(a) Find the mean, variance, and standard deviation of the probability distribution.

(b) Interpret the results.

Hurricanes

123450.00.10.20.30.40.5CategoryProbability0.4070.2870.2260.0680.012

A histogram titled Hurricanes has a horizontal axis labeled Category from 1 to 5 in increments of 1 and a vertical axis labeled Probability from 0 to 0.5 in increments of 0.05. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the category is listed first and the height is listed second: 1, 0.407; 2, 0.287; 3, 0.226; 4, 0.068; 5, 0.012. Each bar is labeled with its height.

(a) The mean is

nothing.

(Type an integer or a decimal. Do not round.)

The variance is

nothing.

(Round to two decimal places as needed.)

The standard deviation is

nothing.

(Round to two decimal places as needed.)

(b) Interpret the results. Select all that apply.

The typical hurricane deviates from the mean by about 1 category level.

The average hurricane is approximately category 1.

The average hurricane is approximately category 2.

The typical hurricane deviates from the mean by about 2 category levels.

Question Help
The histogram shows the distribution of hurricanes that have hit a country from 1851 through 2015, where 1 is the
weakest level and 5 is the strongest level.
Hurricanes
0.5- 0.407
0.4-
0.31
0.21
0.14
0.0
(a) Find the mean, variance, and standard deviation of the probability distribution.
(b) Interpret the results.
0.287
0.226
0.068
0.012
Category
(a) The mean is.
(Type an integer or a decimal. Do not round.)
The variance is.
(Round to two decimal places as needed.)
The standard deviation is.
(Round to two decimal places as needed.)
(b) Interpret the results. Select all that apply.
O A. The typical hurricane deviates from the mean by about 1 category level.
O B. The average hurricane is approximately category 1.
O C. The average hurricane is approximately category 2.
O D.
The typical hurricane deviates from the mean by about 2 category levels.
Probability

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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