Question
?Variation: A measure of the amount that the data values
vary.
?Distribution: The nature or shape of the spread of the data
over the range of values (such as bell-shaped).
?Outliers: Sample values that lie very far away from the vast
majority of the other sample values.
?Time: Any change in the characteristics of the data over
time.
?2.2 Frequency Distributions
?Definitions
?A frequency distribution (or frequency table) shows how data
are partitioned among several categories (or classes) by listing
the categories along with the number (frequency) of data values in
each of them. ?Lower class limits are the smallest numbers that can
belong to the different classes.
?Upper class limits are the largest numbers that can belong
to the different classes.
?Definitions
?Class boundaries are the numbers used to separate the
classes, but without the gaps created by class limits.
?Class midpoints are the values in the middle of the classes.
Each midpoint is computed by adding the lower class limit to the
upper class limit and dividing the sum by 2.
?Class width is the difference between two consecutive lower
class limits in a frequency distribution.
Procedure for Constructing a Frequency Distribution
?Step 1: Select the number of classes, usually between
5 and 20.
?Step 2: Calculate the class width.
?Step 3: Choose the value for the first lower class limit by
using the minimum value.
?Step 4: Using the first lower class limit and the class
width, list the other lower class limits.
?Step 5: List the lower class limits in a vertical column and
then determine and then enter the upper class limits.
?Step 6: Take each individual data value and put a tally mark
in the appropriate class.
Example
?The following represents the ages of the 50 richest
people in the word in
2009.89,89,87,86,86,85,83,83,82,81,80,78,78,77,76,73,73,73,72,69,69,68,67,66,66,65,65,64,63,61,61,60,59,58,57,56,54,54,53,53,51,51,49,47,46,44,43,42,36,35
Construct a frequency distribution by using eight classes.
?Definitions
?A relative frequency of a class is the percentage of the
data that falls in that classes. To find the relative frequency of
a class, divide the frequency of the class by the sum of the
frequencies.
?A cumulative frequency of a class is the sum of the
frequencies of that classes and all previous classes. The
cumulative frequency of the last class is equal to the sum of the
frequencies.
Construct the relative frequency distribution and cumulative
frequency distribution for the previous example.
2.3 Histograms
?DefinitionA histogramis a graph consisting of bars of
equal width drawn adjacent to each other( unless there are gaps in
the data). Horizontal Scale: Use class boundaries or class
midpoints.
Vertical Scale: Use the class frequencies.A relative
frequency histogram has the same shape and horizontal scale as a
histogram, but the vertical scale uses relative frequencies as
percentages.
Critical Thinking: Interpreting Histograms
?Normal DistributionA key characteristic of a normal
distribution is that when graphed as a histogram, the result has a
“bell” shape. We say that the distribution is normal because it is
bell-shaped.
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