Transcript MODE - Gordon State College

Unit 6A
Characterizing a Data
Distribution
DISTRIBUTION
The distribution of a variable (or data set)
describes the values taken on by the variable
and the frequency (or relative frequency) of
these values.
However, much of the time we are less interested
in the complete distribution than in a few
descriptive terms that summarize it.
AVERAGE
There a three different terms that characterize the
center of a data distribution. Any of these can be
called the “average.”
• Mean
• Median
• Mode
MEAN
The mean is defined as:
sum of all values
mean 
total number of values
The mean is what we most commonly refer to as
the average value.
EXAMPLE
The given values are the numbers of Dutchess
County car crashes for each month in a recent
year. Find the mean.
27 8 17 11 15 25 16 14 14 14 13 18
MEDIAN
The median is the middle value in a sorted data
set (or halfway between the two middle values if
the number of values is even).
6.72
3.46
3.60
6.44
3.46
3.60
6.44
6.72
(even number of values)
no exact middle -- shared by two numbers
3.60 + 6.44
MEDIAN is 5.02
2
6.72
3.46
3.60
6.44
26.70
3.46
3.60
6.44
6.72
26.70
(in order -
exact middle
odd number of values)
MEDIAN is 6.44
EXAMPLE
The given values are the numbers of Dutchess
County car crashes for each month in a recent
year. Find the median.
27 8 17 11 15 25 16 14 14 14 13 18
MODE
• The mode is the most common value (or
group of values) in a distribution.
• When two values occur with the same
greatest frequency, each one is a mode and
the data set is said to be bimodal.
• When more than two values occur with the
same greatest frequency, each is a mode and
the data set is said to be multimodal.
EXAMPLE
a. 5 5 5 3 1 5 1 4 3 5
Mode is 5
b. 1 2 2 2 3 4 5 6 6 6 7 9
Bimodal -
c. 1 2 3 6 7 8 9 10
No Mode
2 and 6
EXAMPLE
The given values are the numbers of Dutchess
County car crashes for each month in a recent
year. Find the mode.
27 8 17 11 15 25 16 14 14 14 13 18
FINDING THE MEAN AND
MEDIAN ON THE TI-83/84
1. Press STAT; select 1:Edit….
2. Enter your data values in L1. (You may enter the
values in any of the lists.)
3. Press 2ND, MODE (for QUIT).
4. Press STAT; arrow over to CALC. Select 1:1-Var
Stats.
5. Enter L1 by pressing 2ND, 1.
6. Press ENTER.
7. The mean is the number after x=.
8. Scroll down using the down arrow key to find the
median. It is on the line Med=.
FINDING THE MODE
ON THE TI-83/84
The TI-83/84 will NOT calculate the mode of a
data set. However, the data in a list can be easily
sorted to help in finding the mode.
To sort L1 in ascending (lowest to highest) order:
STAT, 2:SortA, L1, ), and ENTER.
To sort in descending (highest to lowest) order,
use 3:SortD.
OUTLIER
An outlier is a data value that is much higher or
lower than almost all other values.
Outliers usually have a drastic affect on the mean.
However, outliers do not affect the median or the
mode.
SYMMETRIC
A distribution is symmetric if its left half is a
mirror image of its right half.
NOTE: The mean,
median, and mode are
equal.
Mode
=
Mean
=
Median
SYMMETRIC
LEFT-SKEWED
A distribution is left-skewed if its values are more
spread out on the left side. Another term for leftskewed is negatively-skewed.
Mean
Mode
Median
LEFT-SKEWED
(negatively)
NOTE: The mean is on
the left; the mode on the
right; and the median in
between the mean and
mode.
RIGHT-SKEWED
A distribution is right-skewed if its values are
more spread out on the right side. Another term
for right-skewed is positively-skewed.
Mean
Mode
Median
RIGHT-SKEWED
(positively)
NOTE: The mode is on
the left; the mean on the
right; and the median in
between the mean and
mode.
VARIATION
Variation describes how widely data values are
spread out about the center of a distribution.