Organizing Raw Data, Summaries of Statistics

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Organizing Raw Data

What is a Raw Data?

Raw Data (sometimes called source data) is data that has not been processed for meaningful use.

What is a Frequency Distribution Table?

A Frequency Distribution Table is one way that we can organize raw data so that it makes more sense and will give us a better picture of our obtained data than simply a list.

We label Columns of a frequency distribution table as follows and we use combination of these columns to construct different statistical drawing:

Class Limits Class Boundaries Class Midpoints Class Frequencies Cumulative Frequencies Relative Frequencies Percentage Frequencies

Here is an example of Frequency Distribution Table :

Class Class Class Class Cumulative Relative Percentage Limits Boundaries Midpoint Frequency Frequency Frequency Frequency

Always sort the raw data in ascending order before you

start building the frequency distribution table.

To make a Frequency Distribution Table , we first need to find its Class Width.

How do we find the Class Width?

Here are some steps that we need to take:

(^1) Sort the raw data (^2) Find the minimum and maximum value of the raw data (^3) Find the range, Range = Max − Min (^4) Find class width, CW = Range number of classes ◮ (^) when CW is a whole number, add 1. ◮ (^) When CW is a decimal number, round up.

Objective:

(^1) Find the minimum and the maximum value. (^2) Find the value of the range. (^3) Find the class width if we wish to have a frequency distribution table with 5 classes.

Solution:

Since our data is already sorted in ascending order, then we can easily discover that Min.= 53, Max.= 100, Range = Max. − Min. = 100 − 53 = 47,

Class Width =

Range Number of Classes

= 9. 4 ⇒ CW= 10

Objective:

Find all lower class limits.

Solution:

(^1) We begin by choosing the minimum value 53 as our first lower class limit (^2) To find the rest of lower class limits, we just add the class width to each lower class limit in order to get the next lower class limit. Second Lower Class Limit = 53 + 10 = 63 Third Lower Class Limit = 63 + 10 = 73 Fourth Lower Class Limit = 73 + 10 = 83 Fifth Lower Class Limit = 83 + 10 = 93

(^3) So our lower class limits are 53, 63, 73, 83, and 93.

How do we find the Upper Class Limits?

Here are some steps that we need to take for the raw data with D decimal places: (^1) First Upper Class Limit = First Lower Class Limit + Class Width −. 1 D (^2) Second Upper Class Limit = First Upper Class Limit + Class Width (^3) Third Upper Class Limit = Second Upper Class Limit + Class Width (^4) Fourth Upper Class Limit = Third Upper Class Limit + Class Width (^5) And so on.

Solution Continued:

(^2) To find the rest of upper class limits, we just add a multiple of the class width to the first upper class limit in order to get the next upper class limit. Second Upper Class Limit = 62 + 10 = 72 Third Upper Class Limit = 72 + 10 = 82 Fourth Upper Class Limit = 82 + 10 = 92 Fifth Upper Class Limit = 92 + 10 = 102

(^3) So our upper class limits are 62, 72, 82, 92, and 102.

Warning: It is extremely important to make sure

that class width, first lower class limit, and first upper class limit have been calculated correctly.

We are now ready with our class limits to update our Frequency

Distribution Table :

Class Class Class Class Cumulative Relative Percentage Limits Boundaries Midpoint Frequency Frequency Frequency Frequency

Objective:

Find all class boundaries.

Solution:

(^1) First Upper Class Boundary = First Upper Class Limit+Second Lower Class Limit 2 = 62+63 2 = 62. 5 (^2) First Lower Class Boundary =First Upper Class Boundary − Class Width = 62. 5 − 10 = 52. 5 (^3) Now add class width to each class boundary to get the successive class boundary.

Here is a complete list of class boundaries for our sample:

52 .5, 62.5, 72.5, 82.5, 92.5, 102. 5

Let’s update our Frequency Distribution Table with class

boundaries:

Class Class Class Class Cumulative Relative Percentage Limits Boundaries Midpoint Frequency Frequency Frequency Frequency

Objective:

Find all class midpoints.

Solution:

(^1) First Class Midpoint =

(^2) Second Class Midpoint = 57.5 + 10 = 67. 5

(^3) Third Class Midpoint = 67.5 + 10 = 77. 5

(^4) Fourth Class Midpoint = 77.5 + 10 = 87. 5

(^5) Fifth Class Midpoint = 87.5 + 10 = 97. 5

Let’s update our Frequency Distribution Table with class

midpoints:

Class Class Class Class Cumulative Relative Percentage Limits Boundaries Midpoint Frequency Frequency Frequency Frequency