Answered: Here are summary statistics of the four…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.1: Sequences And Their Notations

Problem 5SE: What is a factorial, and how is it denoted? Use an example to illustrate how factorial notation can...

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Question

Here are summary statistics of the four last digits of social security number of 500 customers, corresponding to the following histogram.

Is the mean or median a "better" summary of the center of the distribution?

choose the best answer for the question above:

a. Neither, because these are not quantitative data.

b. Median, because of the outliers.

c. Mean, because the distribution is quite symmetric.

D. Median, because the IQR is smaller than the standard deviation.

e. Neither, because these are not categorical data.

80-
Count
500
Mean
4931
60-
StdDev
1580
Median
IQR
Q1
Q3
5009
2009
4044
6053
40-
20-
1500
4000
6500
9000
Four Last Digits of Social Security Number
#of Customers

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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