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statics chapter 2 methods of data pre, Lecture notes of Statics

Hawassa UniversityStatics

chapter 2 method of data presentation for engineering student

Typology: Lecture notes

2018/2019

Uploaded on 01/25/2019

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CHAPTER 2
2. METHODS OF DATA PRESNTATION
Having collected and edited the data, the next important step is to organize it. That is to
present it in a readily comprehensible condensed form that aids in order to draw
inferences from it. It is also necessary that the like be separated from the unlike ones.
The presentation of data is broadly classified in to the following two categories:
•Tabular presentation
•Diagrammatic and Graphic presentation.
The process of arranging data in to classes or categories according to similarities
technically is called classification.
Classification is a preliminary and it prepares the ground for proper presentation of data.
Definitions:
•Raw data: recorded information in its original collected form, whether it is
counts or measurements, is referred to as raw data.
• Frequency: is the number of values in a specific class of the distribution.
•Frequency distribution: is the organization of raw data in table form using
classes and frequencies.
There are three basic types of frequency distributions
■Categorical frequency distribution
■Ungrouped frequency distribution
■Grouped frequency distribution
There are specific procedures for constructing each type.
•.1. Categorical frequency Distribution
Used for data that can be place in specific categories such as nominal, or ordinal. e.g. marital
status.
Example: a social worker collected the following data on marital status for 25
persons.(M=married, S=single, W=widowed, D=divorced)
MS D W D
S S M M M
W D S M M
W D D S S
S W W D D
Solution:
Since the data are categorical, discrete classes can be used. There are four types of marital
status M, S, D, and W. These types will be used as class for the distribution. We follow
procedure to construct the frequency distribution.
Step 1: Make a table as shown.
Class
(1)
Tally
(2)
Frequency
(3)
Percent
(4)
M
Lecture notes on Introduction to Statistics Chapter 2 METHODS OF
DATA PRESNTATION
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CHAPTER 2

2. METHODS OF DATA PRESNTATION

Having collected and edited the data, the next important step is to organize it. That is to present it in a readily comprehensible condensed form that aids in order to draw inferences from it. It is also necessary that the like be separated from the unlike ones. The presentation of data is broadly classified in to the following two categories:

  • Tabular presentation
  • Diagrammatic and Graphic presentation. The process of arranging data in to classes or categories according to similarities technically is called classification. Classification is a preliminary and it prepares the ground for proper presentation of data. Definitions:
  • Raw data : recorded information in its original collected form, whether it is counts or measurements, is referred to as raw data.
  • F requency : is the number of values in a specific class of the distribution.
  • Frequency distribution : is the organization of raw data in table form using classes and frequencies. There are three basic types of frequency distributions ■ Categorical frequency distribution ■ Ungrouped frequency distribution ■ Grouped frequency distribution There are specific procedures for constructing each type. •.1. Categorical frequency Distribution Used for data that can be place in specific categories such as nominal, or ordinal. e.g. marital status. Example: a social worker collected the following data on marital status for 25 persons.(M=married, S=single, W=widowed, D=divorced) M S^ D^ W^ D S S M M M W D S M M W D D S S S W W D D Solution: Since the data are categorical, discrete classes can be used. There are four types of marital status M, S, D, and W. These types will be used as class for the distribution. We follow procedure to construct the frequency distribution. Step 1: Make a table as shown. Class (1)

Tally (2)

Frequency (3)

Percent (4) M

DATA PRESNTATION

S

D

W

Step 2: Tally the data and place the result in column (2). Step 3: Count the tally and place the result in column (3). Step 4: Find the percentages of values in each class by using; Where f= frequency of the class, n=total number of value. Percentages are not normally a part of frequency distribution but they can be added since they are used in certain types diagrammatic such as pie charts. Step 5: Find the total for column (3) and (4). Combing the entire steps one can construct the following frequency distribution. Class (1)

Tally (2)

Frequency (3)

Percent (4) M ///// 6 24 S //// // 7 28 D //// // 7 28 W //// 5 24

•.2. Ungrouped frequency Distribution -Is a table of all the potential raw score values that could possible occur in the data along with the number of times each actually occurred. -Is often constructed for small set or data on discrete variable. Steps in constructing ungrouped frequency distribution :

  • First find the smallest and largest raw score in the collected data.
  • Arrange the data in order of magnitude and count the frequency.

DATA PRESNTATION

Page 4 of 12

  • Class boundaries: Separates one class in a grouped frequency distribution from another. The boundaries have one more decimal places than the row data and therefore do not appear in the data. There is no gap between the upper boundary of one class and lower boundary of the next class. The lower class boundary is found by subtracting U/2 from the corresponding lower class limit and the upper class boundary is found by adding U/2 to the corresponding upper class limit.
  • Class width : the difference between the upper and lower class boundaries of any class. It is also the difference between the lower limits of any two consecutive classes or the difference between any two consecutive class marks.
  • Class mark (Mid points): it is the average of the lower and upper class limits or the average of upper and lower class boundary.
  • Cumulative frequency: is the number of observations less than/more than or equal to a specific value.
  • Cumulative frequency above: it is the total frequency of all values greater than or equal to the lower class boundary of a given class.
  • Cumulative frequency below: it is the total frequency of all values less than or equal to the upper class boundary of a given class.
  • Cumulative Frequency Distribution (CFD): it is the tabular arrangement of class interval together with their corresponding cumulative frequencies. It can be more than or less than type, depending on the type of cumulative frequency used.
  • Relative frequency (rf): it is the frequency divided by the total frequency.
  • Relative cumulative frequency (rcf): it is the cumulative frequency divided by the total frequency. Guidelines for classes
    1. There should be between 5 and 20 classes.
    2. The classes must be mutually exclusive. This means that no data value can fall into two different classes
    3. The classes must be all inclusive or exhaustive. This means that all data values must be included.
    4. The classes must be continuous. There are no gaps in a frequency distribution.
    5. The classes must be equal in width. The exception here is the first or last class. It is possible to have an "below ..." or "... and above" class. This is often used with ages.

Steps for constructing Grouped frequency Distribution

  1. Find the largest and smallest values
  2. (^) Compute the Range(R) = Maximum - Minimum
  3. Select the number of classes desired, usually between 5 and 20 or use Sturges rule where k is number of classes desired and n is total number of observation.
  4. Find the class width by dividing the range by the number of classes and rounding up, not off..
  5. Pick a suitable starting point less than or equal to the minimum value. The starting point is called the lower limit of the first class. Continue to add the class width to this lower limit to get the rest of the lower limits.

DATA PRESNTATION

Page 4 of 12

  1. To find the upper limit of the first class, subtract U from the lower limit of the second class. Then continue to add the class width to this upper limit to find the rest of the upper limits.
  2. Find the boundaries by subtracting U/2 units from the lower limits and adding U/ units from the upper limits. The boundaries are also half-way between the upper limit of one class and the lower limit of the next class. !may not be necessary to find the boundaries.
  3. Tally the data.
  4. Find the frequencies.
  5. Find the cumulative frequencies. Depending on what you're trying to accomplish, it may not be necessary to find the cumulative frequencies.
  6. If necessary, find the relative frequencies and/or relative cumulative frequencies Example*: Construct a frequency distribution for the following data. 11 29 6 33 14 31 22 27 19 20 18 17 22 38 23 21 26 34 39 27 Solutions: Step 1: Find the highest and the lowest value H=39, L= Step 2: Find the range; R=H-L=39-6= Step 3: Select the number of classes desired using Sturges formula; =1+3.32log (20) =5.32=6(rounding up) Step 4: Find the class width; w=R/ k= 33/6=5.5=6 (rounding up)

Step 5: Select the starting point, let it be the minimum observation. ■ 6, 12, 18, 24, 30, 36 are the lower class limits. Step 6: Find the upper class limit; e.g. the first upper class=12-U=12-1= ■ 11, 17, 23, 29, 35, 41 are the upper class limits. So combining step 5 and step 6, one can construct the following classes. Class limits 6 – 11 12 – 17 18 – 23 24 – 29 30 – 35 36 – 41 Step 7: Find the class boundaries; E.g. for class 1 Lower class boundary=6-U/2=5. Upper class boundary =11+U/2=11.

  • Then continue adding w on both boundaries to obtain the rest boundaries. By doing so one can obtain the following classes. Class boundary

DATA PRESNTATION