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Name: Discuss the characteristics of the basic descriptive statistics: sampl
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Description: Discuss the characteristics of the basic descriptive statistics: sample size, mean, and standard devation.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 6SGR

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Discuss the characteristics of the basic descriptive statistics: sample size, mean, and standard devation.

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

Characteristics of mean:

Mean represents all the values of the data.
Outliers of the data affects the mean.
The sum of deviations about mean is zero.

Step 2

Characteristics of standard deviation:

It describes the variation in data.
It measures the spread of data about the mean.
It can never be negative.
It is sensitive to outliers.
The small value of standard deviation tells that the values of data tends to be very close to each other.

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