Download Measures of Central Tendency

Statistics
Assumed you have had this in
previous math classes…
What are measures of central tendency?
How do you tell measures of central tendency
apart?
What is standard deviation? How is it
calculated?
An intro to Statistics
• Statistics – numerical values used to
summarize & compare sets of data (such
as ERA in baseball).
• Measures of Central Tendency – mean,
median, & mode are the 3 we will be
using. Tells you what the “center” of the
data is.
Mean – ( x ) average of n numbers
(add all #s & divide by n)
Median – the middle # when the #s are
written in order from least to greatest
or greatest to least. If there are 2
middle numbers, the median will be
the average of those 2.
Mode – the number(s) that occur most
frequently. It is possible to have more
than 1 mode or even no mode.
Ex: Find the mean, median, & mode of
the following set of numbers: 36, 39, 40,
34, 48, 33, 25, 30, 37, 17, 42, 40, 24.
• Mean -
445
 34.2
13
Median – Put the numbers in order first!
17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 40, 42, 48
Mode – most frequent!
40 is the mode.
Measures of Dispersion – tell how
spread out the data are.
* Range – Difference between the
largest and smallest values.
(for example: the range of the last
example would be 48-17=31)
* Standard Deviation - (σ – “sigma”)
( x1  x) 2  ( x2  x) 2  ...  ( xn  x) 2 x is the mean

n
x1, x2, x3, …, xn
are the entries in
the data set.
n is the number of entries in the set
x is the mean
Standard Deviation symbol - (σ – “sigma”)
Standard deviation describes the typical difference
(deviation) between the mean and a data value.
“A low standard deviation indicates that the data points
tend to be very close to the mean; high standard
deviation indicates that the data points are spread out
over a large range of values.
Standard deviation is commonly used to measure
confidence in statistical conclusions.”
http://en.wikipedia.org/wiki/Standard_deviation
This is why you see standard deviation on test scores.
Ex: Find the standard deviation of the data
from the first example.
(36  34.2) 2  (39  34.2) 2  (40  34.2) 2  ...  (24  34.2) 2

13
856.32

13
  65.87
  8.12
What are measures of central tendency?
Mean, medium and mode
How do you tell measures of central tendency
apart?
Mean=average, median=middle, mode=appears
most often
What is standard deviation? How is it calculated?
Standard deviation=typical difference between
the mean and a data value.
Assignment
Worksheet 7.7