Organizing Data

							Organizing Data
   Suppose a researcher
wished to do a study on the
 number of miles that the
   employees of a large
 department store traveled
    to work each day.
The researcher first would
 have to collect the data.
When data are collected in
 original form, they are
     called raw data.
The raw data for this example.
1    2    6    7    12   13   2    6    9    5

18   7    3    15   15   4    17   1    14   5

4    16   4    5    8    6    5    18   5    2

9    11   12   1    9    2    10   11   4    10

9    18   8    8    4    14   7    3    2    6
             Frequency Distribution
Class Limits
(in miles)                   Tally              Frequency


    1-3              ///// /////                  10
    4-6              ///// ///// ////             14
    7-9              ///// /////                  10
   10-12             ///// /                      6
   13-15             /////                        5
   16-18             /////                        5
                                        Total    50
A frequency distribution is
  the organization of raw
 data in table form, using
 classes and frequencies.
Twenty-five army inductees were
 given a blood test to determine
their blood type. The data set is:
 A       B      B      AB      O

 O      O       B      AB      B

 B       B      O      A       O

 A      O       O      O      AB

 AB      A      O      B       A
        Since the data is categorical,
        discrete classes can be used.

Class       Tally        Frequency   Percentage

A           /////          5           20


B           ///// //       7           28


O           ///// ////     9           36


AB          ////           4           16
                          25          100
When the range of data is
 large, the data must be
grouped into classes that
are more than one unit in
          width.
Number of hours that boat
   batteries lasted:
The lower class limit is 24
The upper class limit is 30
The class boundaries separate the
  classes so there are no gaps.
    Basic rule of class boundaries:
   The class limits should have the same
    decimal place as the data, but the class
    boundaries should have one additional
    place value and end in a 5.
Class width is found by subtracting the lower class
limit of one class from the lower class limit of the
                      next class
The researcher must decide
 how many classes to use
and the width of each class.
 To construct a frequency
 distribution, follow these
            rules:
1. There should be between 5 and
    20 classes.
   Although there is no hard and fast rule for
    the number of classes contained in a
    frequency distribution, it is of the utmost
    importance to have enough classes to
    present a clear description of the collected
    data.
2. The class width should be an
    odd number.
   This ensures that the midpoint of each
    class has the same place value as the
    data. The class midpoint (Xm) is obtained
    by adding the lower and upper boundaries
    and dividing by 2, or adding the lower an
    upper limits and dividing by 2.

   Computer programs don’t follow this rule.
3. The classes must be mutually
   exclusive.
   No overlapping class limits.

   Bad example:            Good example:
       Age                      Age
     10 – 20                   10 – 20
     20 – 30                   21 – 30
     30 – 40                   31 – 40
4. The classes must be continuous.
   Even if no values occur in a given class,
    that class must be included in the
    distribution.

   A class with zero frequency on either end
    can be omitted.
5. The classes must be exhaustive.
   There should be enough classes to
    accommodate all the data.
6. The classes must be equal in
    width.
   This avoids a distorted view of the data.

   One exception occurs when there is an
    open-ended distribution – i.e., it has no
    specific beginning value or no specific
    ending value.
 Data set 3 represents the
 record high temperatures
 for each of the 50 states.
   Construct a frequency
distribution using 7 classes.
                 Step 1
Determine the width of the classes.

   Find the range (highest minus the
    lowest). [34]
   Divide by the number of classes you
    want. [34/7]
   Round up to the nearest whole number.
    [4.9 → 5.0]
                    Step 2
   Determine your lower limit.

   The smallest datum is 100. Let’s start
    there.

   Keep adding the class width to the lower
    class limits until you have 7 classes
                   Step 3
   Determine class boundaries.
                     Step 4
   Tally the data
                    Step 5
   Find the frequencies.
                   Step 6
   Find the cumulative frequencies.
       Assignment
Data set 1, construct a frequency
distribution for the 4 sets of data