The document defines statistical mean, median, and mode. The mean is the average of all values in a distribution. For discrete variables, it is calculated by adding all values and dividing by the number of terms. For continuous variables, it is the expected value obtained by integrating the variable and its probability. The median separates the higher half from the lower half of a distribution. For discrete variables with an odd number of terms, it is the middle value; for an even number, it is the average of the two middle values. For continuous variables, it is the value where the probability of being below or above it is at least 50%. The mode is the most frequent value - the term that occurs most often for discrete variables. Continuous

1. statistical
mean, median,
and mode

2. What are statistical mean, median, and mode?
The terms mean, median, mode, and range describe
properties of statistical distributions. In statistics, a
distribution is the set of all possible values for terms
that represent defined events. The value of a term,
when expressed as a variable, is called a random
variable.

3. There are two major types of statistical
distributions. The first type contains discrete
random variables. This means that every term
has a precise, isolated numerical value. The
second major type of distribution contains a
continuous random variable. A continuous
random variable is a random variable where the
data can take infinitely many values.

4. Mean
The most common expression for the mean of a statistical distribution
with a discrete random variable is the mathematical average of all the
terms. To calculate it, add up the values of all the terms and then divide
by the number of terms. The mean of a statistical distribution with a
continuous random variable also called the expected value, is obtained
by integrating the product of the variable with its probability as defined
by the distribution. The expected value is denoted by the lowercase
Greek letter mu (µ).

5. Median
The median of a distribution with a discrete random variable depends
on whether the number of terms in the distribution is even or odd. If
the number of terms is odd, then the median is the value of the term in
the middle. This is the value such that the number of terms having
values greater than or equal to it is the same as the number of terms
having values less than or equal to it. If the number of terms is even,
then the median is the average of the two terms in the middle, such
that the number of terms having values greater than or equal to it is
the same as the number of terms having values less than or equal to it.

6. The median of a distribution with a continuous
random variable is the value m such that the
probability is at least 1/2 (50%) that a randomly
chosen point on the function will be less than or
equal to m, and the probability is at least 1/2
that a randomly chosen point on the function
will be greater than or equal to m.

7. Mode
The mode of a distribution with a discrete random variable is the value
of the term that occurs the most often. It is not uncommon for a
distribution with a discrete random variable to have more than one
mode, especially if there are not many terms. This happens when two
or more terms occur with equal frequency, and more often than any of
the others. A distribution with two modes is called bimodal. A
distribution with three modes is called trimodal. The mode of a
distribution with a continuous random variable is the maximum value
of the function. As with discrete distributions, there may be more than
one mode

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