Question

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

Answer #1

When a distribution is symmetric, we know that the data is divided in exactly two equal parts. For this symmetric distribution, the probability below the mean and above the mean is equal. Also, we know that the median is the middle most observation when data is in an increasing or decreasing order. For the symmetric distribution, the middle point is exactly located at the place where mean is situated.

The concept is well explained by the following diagram:

Also, we know that the mode is equal to mean and median for the symmetric distribution.

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?

A dot plot is best applied when _____________________.
Select one:
a. The mean, median, and mode are equal
b. The general shape of a distribution is symmetric
c. The relationship between two variables is summarized
d. A single variable is summarized

Why the textbook says that SAT scores is a Symmetric (Unimodal)
distribution?

Why is the median? resistant, but the mean is? not? Choose the
correct answer below. A. The mean is not resistant because it is
dependent upon the sample? size, n. The larger n? is, the smaller
the mean becomes.? However, the median is resistant because it is
not dependent on the sample? size, n. B. The mean is not resistant
because when data are? skewed, there are extreme values in the?
tail, which tend to pull the mean in the...

1. For which type of continuous distribution are the mean and
the median always the same?
uniform and normal distributions only
all of the above
uniform distribution
exponential distribution
normal distribution
2. The skewness of a normal distribution is:
negative
zero
positive
something that varies
3. The standard normal probability distribution has a mean of
______ and a standard deviation of ______.
0, 1
1, 0
1, 1
0, 0
4. Any normal probability distribution can be converted to a...

Skewness in a frequency distribution can be determined by
comparing:
the median to the mean
or
the mode to the median
or
the mean to the mode
or
any two of the three measures of central tendency

In a positively skewed distribution:
a.
the median is less than the mean.
b.
the median equals the mean.
c.
the median is larger than the mean.
d.
the mean can be larger or smaller than the median.
What is the mean of x, given the function below?
f(x) =(1/10)
e-x/10
x 0
a.
100
b.
1,000
c.
10
d.
0.10
The starting salaries of individuals with an MBA degree are
normally distributed with a mean of $40,000 and a...

The distribution of a random variable X is symmetric, with a
mean of 500 and a standard
Deviation of 10. You are asked to provide two numbers such that
about 68% of the values
Of X are between the two numbers. The two numbers are:
a. (400, 600)
b. (490, 510)
c. (480,520)
d. Can’t tell

Use the mean and the median to describe the distribution of
relative skill of your team.
Describe the skew: Is it left, right, or
bell-shaped?
Explain which measure of central tendency is best to use to
represent the center of the distribution based on its
skew.
Statistic Name
Value
Mean
1617.48
Median
1652.57
Variance
9987.20
Standard Deviation
99.94

A collection of data has a bell shaped, symmetric distribution.
The mean of the data is 20 and the standard deviation is 2.
Approximately 95% of the data will fall within the interval;
[4 points]
[14,26][12,28] [18,22][16,24][16,26]

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