Question

How does the mean, median, and mode location differ between a symmetric to skewed distribution?

Why are measure of location, commonly called measures of center, not sufficient in themselves to get a good picture of a data set?

Answer #1

For symmetric distribution

mean= median= mode

For left skewed(-vely skewed)

Mode>Median>Mean

For right skewed(+ve ly skewed)

Mode<Median<Mean

This is how the mean ,median and mode varies with the skewness of the data.

The measure of centres work good when there is no outlier. Due to oultiers we cant get the good picture of a dataset. So we use Q1,Q3 and Inter quartile range to remove the outlier and then calculate the measures of centre to get a good picture.

Mean, median, and mode are the three measures of central
tendency that we learned about in this class. We use these to
describe the center of a distribution. For each of the following
examples please identify which measure of central tendency should
be used given the situation.
A negatively skewed distribution
A platykurtic distribution

1.The median is a measure of central tendency (or
location)?
True
False
2,The mean computed from ungrouped data is a more accurate measure
than the mean computed from grouped data?
True
False
3.The mode for the following values is "0"?...3.4, 4.7, 1.9,
7.6, 6.5.
True
False
4.A distribution of data that is positively skewed is left
skewed?
True
False
5.In a numerical batch of data the value of "Q3" can never be
smaller than the value of "Q1"?
True
False ...

why is the mean and median the same when a distribution is
symmetric?

Which measure of center ( Mean, Median, or Mode) may
not appear in every data set?

The durations (minutes) of 26 electric power outages in the
community of Sonando Heights over the past five years are shown
below. 34 48 25 66 24 9 58 10 52 4 16 47 40 100 32 18 13 49 22 4 17
25 89 28 14 19 Click here for the Excel Data File (a) Find the
mean, median, and mode. (Round your answers to 2 decimal places.)
Descriptive Statistics Data Mean Median Mode (b) Are the mean and...

The durations (minutes) of 26 electric power outages in the
community of Sonando Heights over the past five years are shown
below.
33
47
25
68
25
9
58
9
50
4
16
48
41
100
31
20
13
48
23
3
17
26
88
29
14
18
(a) Find the mean, median, and mode. (Round your
answers to 2 decimal places.)
Descriptive
Statistics
Data
Mean
Median
Mode
(b) Are the mean and median about the same?
(yes...

The three commonly used measures of central tendency
are
mode, median, and mean.
percentage, midpoint, and mean.
mode, midpoint, and ratio.
median, rate, and mode.
T he purpose of univariate descriptive statistics is
to
summarize relationships between many variables.
display the essential meaning of variables measured at the
interval-ratio level.
combine nominal and discrete variables.
summarize a single variable.
The most appropriate measure of central tendency for
gender would be the
median.
mode.
mean.
None of the above
If you...

How does a positively skewed distribution differ in
appearance from a negatively skewed one?

how does a positively skewed distribution differ in
appearance from a negatively skewed one?

The durations (minutes) of 26 electric power outages in the
community of Sonando Heights over the past five years are shown
below.
37
50
23
67
25
13
55
14
49
3
13
41
42
101
30
17
12
52
21
2
17
27
91
26
14
20
(a) Find the mean, median, and mode.
(Round your answers to 2 decimal places.)
(b) Are the mean and median about the
same? (Click to select) Yes
or No , the mean is
greater than...

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