Math Tech IIII, Sep 19
Measures of Central Tendency (Mean, Median,
and Mode, and Mid-Range)
Book Sections: 2.3
Essential Questions: How do I compute and use statistical values?
What are measures of central tendency, and how can I compute and
use them?
Standards: PS.SPID.2
Symbols to Know and Love
• Every statistic has a name and many have
symbols. The ones that are important today
are:
_
Mean =
x
Median = med
Mode – no symbol
Statistical Convention
• Round your computed values to one more
decimal place than is contained in the raw data
 If raw is whole numbers or integers – round to 1-decimal
place
 If raw is decimal data – round to one more place than max
data decimal place
Using Your Calculator
Prompting
calculators:
Computing these statistics by calculator:
•Enter list into L1
•Press [STAT]  {CALC} select 1-Var Stats*
•Look for X as mean, med as median
•Mode – sort list and look for repeats
* In 1-Var Stats, L1 is the default. If using another list,
you must put its name after 1-Var stats
Mean, Median, and Mode
Made Easy
• Mean, Median, and Mode are statistics
called measures of central tendency.
• Measures of Central Tendency are
statistics that show where a middle point
of the data is located.
Rule of Thumb
If you are going to compute the values of
measures of central tendency manually (and I
do not recommend doing this), always
arrange your data set in order as a first step.
Mean
• The mean is the average of a data set. You can find
it by adding all set values and dividing by the
number of data points.
_
Mean (x) =
Sum of data values
Number of data values
Example
• Find the mean of the following data set:
16, 24, 14, 18, 30
Don’t Make It Mean
• We will soon find out that there is more than
one
__
mean. In fact there are two, sample mean x and the
population mean, µ.
• We will learn how they are related later, for now we
are working__with simple computations and we are
computing x .
Median
• The set median is the middle value of the set.
• If there are an odd number of data points, the
median is the middle value when the set is arranged
in order from least to greatest.
• If the set has an even number of data points, the
median is the average of the two middle values when
the set is arranged in order from least to greatest.
Example
• Find the median of the following data set:
16, 24, 14, 18, 30
In order: 14, 16, 18, 24, 30
Example
• Find the median of the following data set:
16, 24, 14, 18, 30, 14
In order: 14, 14, 16, 18, 24, 30
Mode
• The data mode is the number that appears most
often.
•A set can have no mode if no element appears more
than once, or more than one mode if there is a tie for
data points that appear the most.
Example
• Find the mode of the following data set:
16, 24, 14, 18, 30, 14
In order: 14, 14, 16, 18, 24, 30
Example – Compute the Mean, Median, and
Mode of the following data set.
14, 21, 16, 11, 15, 17, 12, 18, 13
Example – Compute the Mean, Median, and
Mode of the following data set by calculator.
50, 32, 64, 35, 41, 57, 55, 46, 21, 31, 51, 68, 39, 40, 45, 28, 56, 64, 58, 36, 27, 44, 49,
54, 65, 43, 42, 38, 47, 37
Mid-Range
• The mid-range is the middle of the data’s range,
Computed by the formula:
Mid-range =
Set Hi + Set Low
2
Example – Compute the Mid-Range of the
following data set
50, 32, 64, 35, 41, 57, 55, 46, 21, 31, 51, 68, 39, 40, 45, 28, 56, 64, 58, 36, 27, 44, 49,
54, 65, 43, 42, 38, 47, 37
Example – Compute the mean, median, mode
and Mid-Range of the following data set
16, 21, 11, 20, 12, 21, 15, 20, 19, 20
Class work: CW 9/19/16, 1-7
Homework: None