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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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