Answered: Neither the mean nor the median will…

Elementary Algebra

17th Edition

ISBN:9780998625713

Author:Lynn Marecek, MaryAnne Anthony-Smith

Publisher:Lynn Marecek, MaryAnne Anthony-Smith

Chapter1: Foundations

Section1.7: Decimals

Problem 1.192TI: Add: 5.123+18.47 .

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Question

The boxplot below displays the average number of jumbo marshmallows consumed in eating contests across a particular state. The higher outlier is from a professional, heavyweight contest, and the lower outliers are from children's eating contests.

What effect will removing all outliers have on the mean and median of the data set?

Neither the mean nor the median will change.

The median will change and the mean will increase.

The median will change and the mean will decrease.

or The mean will remain unchanged and the median will increase.

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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