populationHeight x P (x)x∙P(x)x2x2 ∙ p(x)54 inches 0.052.72916145.858 inches0.052.93364168.260 inches0.2112.6360075661 inches0.3219.5237211190.7262 inches0.116.823844422.8463 inches0.053.153969198.4564 inches0.053.24096204.866 inches0.053.34356217.867 inches0.117.374489493.79 ∑ p(x)= 1∑ x∙P(x)= 61.56 ∑ x2 ∙ p(x) = 3798.4sampling distribution of the sample Valuesfrequencyprobability162.5 11/35262.7511/3536322/35463.2533/35563.544/35663.7544/3576455/35864.2544/35964.544/351064.7533/35116522/351265.2511/351365.511/35Sum 351activity: Compute for the mean (??̅) and standard deviation (??̅) of the sampling distribution of the samplemeans and compare these to the mean and standard deviation of the population.

We know that, Mean = (summation f*x)/(summation f) And standard deviation= √E(X2)-mean2 E(X2)=…

Answered: population Height x P (x) x∙P(x)…

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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population

Height x	P (x)	x∙P(x)	x2	x2 ∙ p(x)
54 inches	0.05	2.7	2916	145.8
58 inches	0.05	2.9	3364	168.2
60 inches	0.21	12.6	3600	756
61 inches	0.32	19.52	3721	1190.72
62 inches	0.11	6.82	3844	422.84
63 inches	0.05	3.15	3969	198.45
64 inches	0.05	3.2	4096	204.8
66 inches	0.05	3.3	4356	217.8
67 inches	0.11	7.37	4489	493.79
	∑ p(x)= 1	∑ x∙P(x)= 61.56		∑ x2 ∙ p(x) = 3798.4

sampling distribution of the sample

	Values	frequency	probability
1	62.5	1	1/35
2	62.75	1	1/35
3	63	2	2/35
4	63.25	3	3/35
5	63.5	4	4/35
6	63.75	4	4/35
7	64	5	5/35
8	64.25	4	4/35
9	64.5	4	4/35
10	64.75	3	3/35
11	65	2	2/35
12	65.25	1	1/35
13	65.5	1	1/35
Sum		35	1

activity:

Compute for the mean (??̅) and standard deviation (??̅) of the sampling distribution of the sample
means and compare these to the mean and standard deviation of the population.

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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