Consider the following Minitab display of two data sets showing: sample size, mean, standard error, standard deviation, minimum, Q1, median, Q3, and maximum. Variable N Mean S.E. StDev Min. Q1 Median Q3 Max. C1 20 20.00 1.62 7.26 7.00 15.0 20.00 25.0 31.00 C2 20 20.00 1.30 5.79 7.00 20.0 22.00 22.0 31.00 (a) What are the respective means? The respective ranges? C1 C2 mean range (b) Which data set seems more symmetric? Why? C2 seems more symmetric because the median is greater than the mean .C1 seems more symmetric because the standard deviation is greater than the standard deviation for C2. C1 seems more symmetric because the mean is equal to the median. C2 seems more symmetric because the interquartile range is smaller than the interquartile range for C1. (c) Compare the interquartile ranges of the two sets. How do the middle halves of the data sets compare? The C1 distribution has a larger interquartile range that is symmetric around the median. The C2 distribution has a smaller interquartile range that is symmetric around the median. The C1 distribution has a smaller interquartile range that is symmetric around the median. The C2 distribution has a larger interquartile range that is symmetric around the median.

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

Consider the following Minitab display of two data sets showing:
sample size, mean, standard error, standard deviation, minimum, Q1, median, Q3, and maximum.

Variable	N	Mean	S.E.	StDev	Min.	Q1	Median	Q3	Max.
C1	20	20.00	1.62	7.26	7.00	15.0	20.00	25.0	31.00
C2	20	20.00	1.30	5.79	7.00	20.0	22.00	22.0	31.00

(a) What are the respective means? The respective ranges?

	C1	C2
mean
range

(b) Which data set seems more symmetric? Why?

C2 seems more symmetric because the median is greater than the mean

.C1 seems more symmetric because the standard deviation is greater than the standard deviation for C2.

C1 seems more symmetric because the mean is equal to the median.

C2 seems more symmetric because the interquartile range is smaller than the interquartile range for C1.

The C1 distribution has a larger interquartile range that is symmetric around the median.

The C2 distribution has a smaller interquartile range that is symmetric around the median.

The C1 distribution has a smaller interquartile range that is symmetric around the median.

The C2 distribution has a larger interquartile range that is symmetric around the median.

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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