Math and Arithmetic

Statistics

Algebra

# Are the mean median and the mode the same in a unimodal symmetrical distribution?

###### Wiki User

###### October 28, 2008 8:25PM

No they are not the same in a unimodal symmetrical distribution

and they will never be

## Related Questions

###### Asked in Salary and Pay Rates, Statistics

### Is the mean and median similar?

The Mean is the average of a given set of values. The Median is
the value that has
the same number of smaller values than the number of higher
values, it is in the
middle of them. In a symmetrical distribution the Mean is equal
to the Median. In an
asymmetrical distribution they have different value.

###### Asked in Math and Arithmetic, Statistics

### What is the nature of symmetry if median is greater than the mean?

Generally, when the median is greater than the mean it is
because the distribution is skewed to the left. This results in
outliers or values further below the median than above the median
which results in a lower mean value than median value. When a
distribution is skewed left, it is generally not very symmetrical
or normally distributed.

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### What can the difference between mean and median values infer. If the mean is 8 655.7 and the median -8 653.0?

First, I will give an example, similar to your question: -11000
-9000 +44000 mean = 8,000 and median = -9000. Symmetrical
distributions after infinite sampling will show no difference in
mean and median. Large differences are possible with small sample
sizes even with symmetrical distributions. If the sample is large
and the difference is large, this infers that the distribution is
asymmetrical. The skewness of the distribution can be
calculated.

###### Asked in Math and Arithmetic, Statistics, Algebra

### Is Mean is more sensitive to skewness than the median?

If the distribution is positively skewed , then the mean will
always be the highest estimate of central tendency and the mode
will always be the lowest estimate of central tendency (If it is a
uni-modal distribution). If the distribution is negatively skewed
then mean will always be the lowest estimate of central tendency
and the mode will be the highest estimate of central tendency.
In both positive and negative skewed distribution the median
will always be between the mean and the mode. If a distribution is
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###### Asked in Statistics

### What is unimodel?

###### Asked in Math and Arithmetic, Statistics, Probability

### Is normal distribution symmetrical?

Yes. By definition. A normal distribution has a
bell-shaped density curve described by its mean and
standard deviation. The density curve is symmetrical
(i.e., an exact reflection of form on opposite sides of a dividing
line), and centered about (divided by) its mean, with its spread
(width) determined by its standard deviation. Additionally, the
mean, median, and mode of the distribution are equal and located at
the peak (i.e., height of the curve).

###### Asked in Math and Arithmetic, Statistics, Algebra

### When you calculate mean is the answer same when the same data is calculated by median?

No.
The mean and median are not necessarily the same. They will be
the same if the distribution is symmetric but the converse is not
necessarily true. That is to say, a distribution does not have to
be symmetric for the mean and median to be the same.
For example, the mean and median of {1, 1, 5, 6, 12} are both 5
but the distribution is NOT symmetric.

###### Asked in Math and Arithmetic, Statistics, Probability

### What is the mean of a normal distribution?

It is the expected value of the distribution. It also happens to
be the mode and median.
It is the expected value of the distribution. It also happens to be
the mode and median.
It is the expected value of the distribution. It also happens to be
the mode and median.
It is the expected value of the distribution. It also happens to be
the mode and median.