Central Tendency Measures of central tendency are used to
display the idea of centralness for a data set. Most common
measures Mean Median Mode Midpoint Midrange
Slide 3
Median MD Median is the middle value in a distribution when all
values are rank ordered. It is not influenced by extreme values. It
simply divided the upper half of the distribution from the lower
half.
Slide 4
Properties of Median Median is used to find the center of the
data set Can use the median to determine if values fall in the
upper or lower portion of the data set Median is not really
affected by outliers that are extremely high or low
Slide 5
Median Rule of Thumb Which value is the Median? The rule of
thumb for calculating the median is this: The median is observation
(n+1)/2 Order the observations Calculate (n+1)/2 Count the data
values (x) until you find that observation If you get a.5, the
median is the average of those two values Ex n = 8: Median value is
(8+1)/2 = 4.5 The Median is the average of the 4 th and 5 th
observations n = 7: Median value is (7+1)/2 = 4 The Median is the 4
th observation
Slide 6
Median Examples Data set is: 3, 5, 7, 7, 8 n = 5 Median value
is 5+1/2 = 3 rd value MD = 7 Data set is: 3, 5, 7, 7, 8, 10, 12, 14
n = 8 Median value is 8+1/2 = 4.5 th value 7 + 8 = 15/2 = 7.5 MD =
7.5
Slide 7
Median for Grouped Data You will do the same calculations for
the continuous data Calculate (n+1)/2 However, the observations are
already ordered for us by the frequencies of the classes We find
the observation number by looking at the frequency of the
classes
Slide 8
Grouped Data Set Class (lbs) f 0 44 5 92 10 141 15 190 20 241
Total 8 To Calculate the median, we find (n+1)/2 n = 8 (8+1)/2 =
4.5 It is the average of the 4 th & 5 th observations Use Class
Midpoints for observation values 4 th values is 2 5 th value is 7
Average is (7+2)/2 = 4.5 MD = 4.5 Observations 1, 2, 3, & 4
Observations 5 & 6 Observation 7 Observation 8 XmXm 2 7 12 17
22
Slide 9
Mode The mode is the most frequent observation. The
distribution may have several modes or no modes. Only measure of
central tendency that can be used for categorical data Types of
Modes Unimodal one mode Bimodal two modes two values that occur
with identical highest frequency Multimodal more than two modes No
mode every observation occurs only once
Grouped Data Instead of a mode, we have a modal class Determine
the class with the highest frequency The modal class is 0 4 Class
(lbs)f 0 44 5 92 10 141 15 190 20 241 Total 8
Slide 14
Midrange The midrange, MR, is a more rough estimate of the
middle of the data set Found by taking the average of the highest
and the lowest values Affected by outliers
Slide 15
Midrange Examples Data set is: 3, 5, 7, 7, 8 Midrange value is
(8 + 3)/2 = 5.5 MR = 5.5 Data set is: 3, 5, 7, 7, 8, 10, 12, 14
Midrange value is (14 + 3)/2 = 8.5 MR = 8.5
Slide 16
Distribution When the mean, median, and mode are all at the
same point, the center of the distribution, the data is considered
to be symmetrically or normally distributed.
Slide 17
When data is skewed, values have bunched up at one end or the
other. With skewed data, the mean, median, and mode are usually all
different values (spread apart). The distribution of the data can
be positively or negatively skewed. Distribution
Slide 18
Positively skewed distribution (Mode < Median < Mean) A
distribution in which the majority of the data values fall to the
left of (below) the mean. The tail of the data trails to the upper
end of the values Distribution
Slide 19
Negatively skewed distribution (Mean < Median < Mode) A
distribution in which the majority of the data values fall to the
right of (above) the mean. The tail of the data trails to the lower
values of the data Distribution
