Transcript Section 2.3 Measures of Central Tendency Statistics Mrs. Spitz Fall 2008 Objectives: § How to find the mean, median and mode of a population and a sample §

Section 2.3
Measures of Central
Tendency
Statistics
Mrs. Spitz
Fall 2008
Objectives:
§ How to find the mean, median and mode
of a population and a sample
§ How to find a weighted mean and the
mean of a frequency distribution
§ How to describe the shape of a distribution
as symmetric, uniform or skewed.
Assignment: pp. 62-66 #1-42
Larson/Farber Ch 2
Measure of central tendency
§ Is a value that represents a typical, or
central entry of a data set. The three most
commonly used measures of central
tendency are mean, median, and the
mode.
Larson/Farber Ch 2
Symbol Description
§ It would be a good idea now to start
looking at the symbols which will be part of
your study of statistics.
 The uppercase Greek letter sigma; indicates a
X
N

x
summation of values
A variable that represents quantitative data
Number of entries in a population
The lowercase Greek letter mu; the population mean
Read as “x bar;” the sample mean
Larson/Farber Ch 2
Measures of Central Tendency
Mean: The sum of all data values divided by the number
of values
For a population:
For a sample:
Median: The point at which an equal number of values
fall above and fall below
Mode: The value with the highest frequency
Larson/Farber Ch 2
An instructor recorded the average number of
absences for his students in one semester. For a
random sample the data are:
2 4 2 0 40 2 4 3 6
Calculate the mean, the median, and the mode
Mean:
Median:
Sort data in order
0 2 2 2 3 4
4
6
40
The middle value is 3, so the median is 3.
Mode:
The mode is 2 since it occurs the most times.
Larson/Farber Ch 2
Suppose the student with 40 absences is dropped from the
course. Calculate the mean, median and mode of the remaining
values. Compare the effect of the change to each type of average.
2 4 2 0 2 4 3 6
Calculate the mean, the median, and the mode.
Mean:
Median:
Sort data in order.
0 2 2 2 3 4 4
6
The middle values are 2 and 3, so the median is 2.5.
Mode:
The mode is 2 since it occurs the most times.
Larson/Farber Ch 2
Weighted Mean and Mean of Grouped Data
§ Sometimes data sets contain entries that
have a greater effect on the mean than do
other entries. To find the mean of such
data sets, you must find the weighted
The weighted mean is the
mean.
( x  w)

x
w
Larson/Farber Ch 2
mean of a data set whose
entries have varying
weights. A weighted
mean is given by the
equation to the left where
w is the weight of each
entry x.
Mean of Grouped Data
§ The mean of a frequency distribution for a
sample is approximated by:
(x  f )

x
n
Where x and f are the midpoints and
frequencies of a class, respectively.
Larson/Farber Ch 2
Finding the mean of a frequency distribution
1. Find the midpoint of each class.
2. Find the sum of the products of the
midpoints and the frequencies.
3. Find the sum of the frequencies
4. Find the mean of the frequency
distribution.
Larson/Farber Ch 2
Shapes of Distributions
Symmetric
Uniform
Mean = Median
Skewed right
Mean > Median
Larson/Farber Ch 2
Skewed left
Mean < Median