A weighted, single six-sided die is rolled 100 times, and the results are given in the table below.Outcome123456Frequency131219171920 (a) Find the mean outcome value (round to two decimal places). (b) Find the sample standard deviation of the outcome values (round to 2 decimal places).

Given : X Frequency 1 13 2 12 3 19 4 17 5 19 6 20 solution : Solution: x Frequency (f) f*x f⋅x^2=(f⋅x)×(x) 1 13 13 13 2 12 24 48 3 19 57 171 4 17 68 272 5 19 95 475 6 20 120 720 Total n=100 ∑f⋅x=377 ∑f⋅x2=1699 a) Mean, ˉx=∑f*x/n =377/100=3.77b) sample standard deviation, s = √((∑f⋅x^2-(∑f⋅x)^2/n)/n-1)=√((1699-(377)^2/100)/99) = 1.67

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A weighted, single six-sided die is rolled 100 times, and the results are given in the table below.

Outcome	1	2	3	4	5	6
Frequency	13	12	19	17	19	20

(a) Find the mean outcome value (round to two decimal places).

(b) Find the sample standard deviation of the outcome values (round to 2 decimal places).

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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weighted, single six-sided die is rolled 100 times, and the results are given in the table below. Outcome 1 2 3 4 5 6 Frequency 13 12 19 17 19 20 (a) Find the mean outcome value (round to two decimal places). (b) Find the sample standard deviation of the outcome values (round to 2 decimal places).