8:18AAwww-awn.aleks.comO DESCRIPTIVE STATISTICS= Mean, median, and.Shasia v-The total blood cholesterol level was measured for each of 21 adults. Here are the21 measurements (in mg/dL).132, 144, 151, 153, 165, 167, 176, 180, 184, 184, 184, 194, 195, 196, 196, 210, 211, 214, 219, 234, 241(Send data to ExcelFrequency10-8-6.444-22-125175Cholesterol level (in mg/dL)150200225250OMean(a) For these data, which measures ofcentral tendency take more than one value?Choose all that apply.OMedianOModeONone of these measures(b) Suppose that the measurement 241 (the OMeanlargest measurement in the data set) werereplaced by 351. Which measures of centraltendency would be affected by the change?Choose all that apply.OMedianOModeONone of these measuresOMean(c) Suppose that, starting with the originaldata set, the smallest measurement wereremoved. Which measures of centraltendency would be changed from those ofthe original data set? Choose all that apply.OMedianOModeONone of these measures(d) Which of the following best describes the Negatively skeweddistribution of the original data? Choose only OPositively skewedone.ORoughly symmetrical?ExplanationCheckHill Education. AlI Rights Reserved Terms of Use Privacy Acessibility回日国国回 8:18AAwww-awn.aleks.comO DESCRPTIVE STATISTICS---ShasiaMean, median, and mode: ComparisonsW ATIONThe mean, the median, and the mode are measures of central tendencyof a distribution or data set. Recall that the mean of a data set is thesum of the measurements in the data set divided by the number ofmeasurements in the data set, the median is the "middle" value whenthe data have been ordered, and the mode is the measurement (ormeasurements) with the highest frequency.(a) We're asked which, if any, of the three measures of central tendencydo not exist for the data set. The mean and median always exist for adata set. The mode exists for a data set except in the case that none ofthe measurements in the data set is repeated, that is, in the case thateach number in the data set occurs with frequency one. Such is not thecase for the data set in the problem, so a mode exists. (The mode of thedata set is 69.) Therefore, all three measures of central tendency exist forthe data set.(b) If 33, the smallest measurement in the data set, were replaced by 24,then the mean of the data set would decrease (from about 60.9 to about60.5). In fact, as you can check, replacing any measurement in the originaldata set by any smaller value decreases the mean. However, replacing 33by 24 would not change the median, since the median does not dependon the actual value of the smallest measurement (but only on the factthat the smallest measurement is the smallest measurement). In general, wesay that the median is resistant to extreme values, but the mean is not.The modes for this data set would not change because 33 is not a modeand replacing it by 24, a value not in the original data set, would notaffect the frequency of the other values.(c) If the largest measurement, which is 77, were removed from theoriginal data set, then the mean would necessarily decrease. In fact,removing any measurement larger than the mean of the data set willcause the mean to decrease. (Here, the mean decreases from about 60.9to about 60.1.) In this case, the median also is affected. In particular, themedian changes from 63 to 62 when the measurement is removed. Themode does not change when the measurement is removed.(d) To get an idea of the distribution of the original data, it is helpful tolook at the histogram for the data, which is shown above. Looking at thehistogram, we see that the distribution of data is not symmetrical. Inparticular, the distribution has a noticeable "tail" extending to the left(but no such "tail" extending to the right). This occurs because there areseveral measurements that are quite small relative to the othermeasurements. If a distribution is not symmetrical and if its histogramshows a tail to the left, then the distribution is said to be skewed to theleft, or negatively skewed.O ANSWERMean(a) Which measures of central tendency donot exist for this data set? Choose all thatapply.MedianModeONone of these measures(b) Suppose that the measurement 33 (the Meansmallest measurement in the data set) wereMedianreplaced by 24. Which measures of centraltendency would be affected by the change?ModeChoose all that apply.None of these measures(e) Suppose that, starting with the original OMeandata set, the largest measurement wereremoved. Which measures of centraltendency would be changed from those ofthe original data set? Choose all that apply.OMedianModeNone of these measuresJONegatively skewed(d) Which of the following best describes thedistribution of the original data? Choose only OPositively skewedone.Roughly symmetricalContinue

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Description: 8:18AAwww-awn.aleks.comO DESCRIPTIVE STATISTICS= Mean, median, and.Shasia v-The total blood cholesterol level was measured for each of 21 adults. Here are the21 measurements (in mg/dL).132, 144, 151, 153, 165, 167, 176, 180, 184, 184, 184, 194, 195,

given dataset mean =188.85 median = 189 mode = 184

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The total blood cholesterol level was measured for each of 21 adults. Here are the 21 measurements (in mg/dL). 132, 144, 151, 153, 165, 167, 176, 180, 184, 184, 184, 194, 195, 196, 196, 210, 211, 214, 219, 234, 241 Send data to Excel Frequency 10- 8. 6- 4- 2- 125 175 Cholesterol level (in mg/dL) 150 200 225 250 (a) For these data, which measures of central tendency take more than one value? Choose all that apply. OMean OMedian OMode ONone of these measures (b) Suppose that the measurement 241 (the OMean largest measurement in the data set) were OMedian replaced by 351. Which measures of central tendency would be affected by the change? OMode Choose all that apply. ONone of these measures (c) Suppose that, starting with the original OMean data set, the smallest measurement were removed. Which measures of central tendency would be changed from those of the original data set? Choose all that apply. ONone of these measures OMedian OMode ONegatively skewed (d) Which of the following best describes the distribution of the original data? Choose only OPositively skewed one. ORoughly symmetrical

The total blood cholesterol level was measured for each of 21 adults. Here are the 21 measurements (in mg/dL). 132, 144, 151, 153, 165, 167, 176, 180, 184, 184, 184, 194, 195, 196, 196, 210, 211, 214, 219, 234, 241 Send data to Excel Frequency 10- 8. 6- 4- 2- 125 175 Cholesterol level (in mg/dL) 150 200 225 250 (a) For these data, which measures of central tendency take more than one value? Choose all that apply. OMean OMedian OMode ONone of these measures (b) Suppose that the measurement 241 (the OMean largest measurement in the data set) were OMedian replaced by 351. Which measures of central tendency would be affected by the change? OMode Choose all that apply. ONone of these measures (c) Suppose that, starting with the original OMean data set, the smallest measurement were removed. Which measures of central tendency would be changed from those of the original data set? Choose all that apply. ONone of these measures OMedian OMode ONegatively skewed (d) Which of the following best describes the distribution of the original data? Choose only OPositively skewed one. ORoughly symmetrical

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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Question

8:18
AA
www-awn.aleks.com
O DESCRIPTIVE STATISTICS
= Mean, median, and.
Shasia v
-
The total blood cholesterol level was measured for each of 21 adults. Here are the
21 measurements (in mg/dL).
132, 144, 151, 153, 165, 167, 176, 180, 184, 184, 184, 194, 195, 196, 196, 210, 211, 214, 219, 234, 241
(Send data to Excel
Frequency
10-
8-
6.
4
4
4-
2
2-
125
175
Cholesterol level (in mg/dL)
150
200
225
250
OMean
(a) For these data, which measures of
central tendency take more than one value?
Choose all that apply.
OMedian
OMode
ONone of these measures
(b) Suppose that the measurement 241 (the OMean
largest measurement in the data set) were
replaced by 351. Which measures of central
tendency would be affected by the change?
Choose all that apply.
OMedian
OMode
ONone of these measures
OMean
(c) Suppose that, starting with the original
data set, the smallest measurement were
removed. Which measures of central
tendency would be changed from those of
the original data set? Choose all that apply.
OMedian
OMode
ONone of these measures
(d) Which of the following best describes the Negatively skewed
distribution of the original data? Choose only OPositively skewed
one.
ORoughly symmetrical
?
Explanation
Check
Hill Education. AlI Rights Reserved Terms of Use Privacy Acessibility
回日国国回

8:18
AA
www-awn.aleks.com
O DESCRPTIVE STATISTICS
---
Shasia
Mean, median, and mode: Comparisons
W ATION
The mean, the median, and the mode are measures of central tendency
of a distribution or data set. Recall that the mean of a data set is the
sum of the measurements in the data set divided by the number of
measurements in the data set, the median is the "middle" value when
the data have been ordered, and the mode is the measurement (or
measurements) with the highest frequency.
(a) We're asked which, if any, of the three measures of central tendency
do not exist for the data set. The mean and median always exist for a
data set. The mode exists for a data set except in the case that none of
the measurements in the data set is repeated, that is, in the case that
each number in the data set occurs with frequency one. Such is not the
case for the data set in the problem, so a mode exists. (The mode of the
data set is 69.) Therefore, all three measures of central tendency exist for
the data set.
(b) If 33, the smallest measurement in the data set, were replaced by 24,
then the mean of the data set would decrease (from about 60.9 to about
60.5). In fact, as you can check, replacing any measurement in the original
data set by any smaller value decreases the mean. However, replacing 33
by 24 would not change the median, since the median does not depend
on the actual value of the smallest measurement (but only on the fact
that the smallest measurement is the smallest measurement). In general, we
say that the median is resistant to extreme values, but the mean is not.
The modes for this data set would not change because 33 is not a mode
and replacing it by 24, a value not in the original data set, would not
affect the frequency of the other values.
(c) If the largest measurement, which is 77, were removed from the
original data set, then the mean would necessarily decrease. In fact,
removing any measurement larger than the mean of the data set will
cause the mean to decrease. (Here, the mean decreases from about 60.9
to about 60.1.) In this case, the median also is affected. In particular, the
median changes from 63 to 62 when the measurement is removed. The
mode does not change when the measurement is removed.
(d) To get an idea of the distribution of the original data, it is helpful to
look at the histogram for the data, which is shown above. Looking at the
histogram, we see that the distribution of data is not symmetrical. In
particular, the distribution has a noticeable "tail" extending to the left
(but no such "tail" extending to the right). This occurs because there are
several measurements that are quite small relative to the other
measurements. If a distribution is not symmetrical and if its histogram
shows a tail to the left, then the distribution is said to be skewed to the
left, or negatively skewed.
O ANSWER
Mean
(a) Which measures of central tendency do
not exist for this data set? Choose all that
apply.
Median
Mode
ONone of these measures
(b) Suppose that the measurement 33 (the Mean
smallest measurement in the data set) were
Median
replaced by 24. Which measures of central
tendency would be affected by the change?
Mode
Choose all that apply.
None of these measures
(e) Suppose that, starting with the original OMean
data set, the largest measurement were
removed. Which measures of central
tendency would be changed from those of
the original data set? Choose all that apply.
OMedian
Mode
None of these measures
JONegatively skewed
(d) Which of the following best describes the
distribution of the original data? Choose only OPositively skewed
one.
Roughly symmetrical
Continue

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