For exercise 1. What is the standard error of these measurements and mean value? I have attached example 3 EXERCISES1. Suppose you measure the time that a ball takes to fall from a height of 10.0 m ten times. Yourmeasurements are 1.45 s, 1.39 s, 1.40 s, 1.43 s, 1.41 s, 1.45 s, 1.38 s, 1.42 s, 1.41 s, and 1.55 s.Calculate and express the mean value and the standard error of these measurements in themanner outlined in Example 3. EXAMPLE 3Suppose that you have measured the length of an object seven times and obtained the values shownin the first column of Table 1. Find (a) the mean value of your measurements and (b) the standardarror of the mean value. (c) Use Equation 1 and Equation 6 to express both your mean value and theerrorstandard error of the mean.Table 1X – X;(m)(x – x)²(m²)(m)16.70.10.0116.80.00.0016.60.20.0416.9-0.10.0117.1-0.30.0916.80.00.0016.70.10.01tion

Answered: EXERCISES Suppose you measure the time…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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For exercise 1. What is the standard error of these measurements and mean value?

I have attached example 3

EXERCISES
1. Suppose you measure the time that a ball takes to fall from a height of 10.0 m ten times. Your
measurements are 1.45 s, 1.39 s, 1.40 s, 1.43 s, 1.41 s, 1.45 s, 1.38 s, 1.42 s, 1.41 s, and 1.55 s.
Calculate and express the mean value and the standard error of these measurements in the
manner outlined in Example 3.

EXAMPLE 3
Suppose that you have measured the length of an object seven times and obtained the values shown
in the first column of Table 1. Find (a) the mean value of your measurements and (b) the standard
arror of the mean value. (c) Use Equation 1 and Equation 6 to express both your mean value and the
error
standard error of the mean.
Table 1
X – X;
(m)
(x – x)²
(m²)
(m)
16.7
0.1
0.01
16.8
0.0
0.00
16.6
0.2
0.04
16.9
-0.1
0.01
17.1
-0.3
0.09
16.8
0.0
0.00
16.7
0.1
0.01
tion

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

Step 1

The population parameters are best estimated by sample parameters. The point estimate for population mean can be given by the sample mean. There must be some in estimation of population mean on the basis of sample mean.

This error is termed as Standard error of the mean, it can be given by formula, $S E = \frac{s}{\sqrt{n}}$ .

where,

s be the sample standard deviation.
n be the sample size.

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