2.2. Summarizing quantitative data - THU

2.2. Summarizing quantitative data:

1. Determine the classes:

For quantitative data, we need to define the classes first. There are define the classes for a frequency distribution:

: Determine the number of nonoverlapping classes, usually classes.

: Determine the width of each class, -

steps to to

Note:

The number of classes and the approximate class are determined by trial and error!!

: Determine the class limits: the smallest possible data value should be larger than or equal to the lower class limit while the largest possible data value should be smaller than or equal to the upper class limit.

Example 3: Suppose we have the following data (in days):

We applied the above procedure to this data.

: We choose to be the number of classes.

:

-

= ..

Therefore, we use as the class width.

Step 3:

The classes we choose are

-

-

-

-

-

Note:

The lower class limit in the first class ( ) is smaller than the smallest data value . Also, the upper class limit in the last class ( ) is larger than the largest data

value .

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2. Summarizing quantitative data:

Tabular summary: In addition to frequency, relative frequency and percent frequency, another tabular summary of quantitative data is the cumulative frequency distribution. Cumulative frequency distribution: the number of data items with values less than

or equal to the upper class limit of each class. Graphical display: histogram and ogive

In addition to histogram, another graphical display of quantitative data is ogive. Ogive: the number of data items with values less than or equal to the upper class limit of each class.

-

.

-

.

-

.

-

.

-

.

.

+=

. +. =.

+=

++=

. +. +.

++=

=.

+++

. +. +. +.

+++

=

=.

=

+++

. +. +. +.

+++

+=

+. =

+=

2

The histogram is

8

6

4

2

0

10

15

20

25

30

35

data

The ogive plot is

Ogive plot

20

cumulative frequency

15

10

5

0 0

5

10

15

20

25

30

35

data

Example 4: Suppose we have the following data:

Suppose the number of non-overlapping classes is determined to be . Please construct the frequency distribution table (including frequency, percent frequency, cumulative frequency, and cumulative percent frequency) for the data.

3

[Solution:]

The class width is . Thus,

-

=.

-

(/ )

.

=.

-

(/ )

.

=.

-

(/ )

.

=.

-

(/ )

..

=.

-

(/ )

=.

4

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