Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower...

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Biostatistics Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari

Transcript of Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower...

Page 1: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Biostatistics

Lecture 3

Prepared by Dr. Ibrahim AL-Jaafari

Page 2: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Organizing and Displaying Data

Quantitative Data

• Frequency Distributions

• Constructing Frequency Distribution Tables

• Relative and Percentage Distributions

• Graphing Grouped Data

• Histograms

• Polygons

Page 3: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Frequency Distributions

Definition

A frequency distribution for quantitative data lists all the

classes and the number of values that belong to each class.

Data presented in the form of a frequency distribution are

called grouped data.

Page 4: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Class Boundary

Definition

The class boundary is given by the midpoint of the

upper limit of one class and the lower limit of the

next class.

Page 5: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Class Boundary

• Class boundary for first class (0-9)

= 9 + 10 / 2 = 9.5

• Class boundary for first class (10-19)

= 19 + 20 / 2 = 19.5

• Class boundary for first class (20-29)

= 29 + 30 / 2 = 29.5

Page 6: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Class Width – Class Size

• The difference between the two boundaries of the class

Class width = Upper Boundary – Lower Boundary

Page 7: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Class Width – Class Size

Class width for the first class (0-9)

= 9.5 – 0.5 = 9

=19.5 – 10.5 = 9

= 29.5 – 20.5 = 9

= 39.5 – 30.5 = 9

= 49.5 – 40.5 = 9

Page 8: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Calculation of Class Width

• Approximate Class Width = 𝑳𝒂𝒓𝒈𝒆𝒔𝒕 𝒗𝒂𝒍𝒖𝒆 −𝑺𝒎𝒂𝒍𝒆𝒔𝒕 𝒗𝒂𝒍𝒖𝒆

𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝑪𝒍𝒂𝒔𝒔𝒆𝒔

Page 9: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Example for Calculation of Class Width

Construct a frequency distribution table for these data

8, 25, 11, 15, 29, 22, 10, 5, 17, 21, 22, 13, 26, 16, 18, 12, 9, 26, 20,

16, 23, 14, 19, 23, 20, 16, 27, 16, 21, 14

Page 10: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Solution

Maximum value = 29 Minimum value = 5

Suppose we decide to group these data using five classes of equal

width

Approximate Class Width = 29 – 5 / 5 = 4.8

5–9, 10–14, 15–19, 20–24, and 25–29

Page 11: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Class Width Table

5 - 9

10 - 14

15 – 19

20 – 24

25 - 29

Page 12: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Class Midpoint – Mark

Calculating Class Midpoint or Mark

Class Midpoint or Mark = 𝑳𝒐𝒘𝒆𝒓 𝒍𝒊𝒎𝒊𝒕+𝑼𝒑𝒑𝒆𝒓 𝑳𝒊𝒎𝒊𝒕

𝟐

Page 13: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Class Midpoint Class Mark

• Class Midpoint

• 0 + 9 / 2 = 4.5

• 10 + 19 / 2 = 14.5

• 49 / 2 = 24.5

• 69 / 2 = 34.5

Page 14: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Relative Frequency and Percentage

Distributions

What is cumulative frequency distribution ??

The total number of values that fall below the upper boundary of each class

What is cumulative relative frequency ??

Cumulative frequency ÷ Total observations in the data set

What is cumulative percentage ??

Cumulative relative frequency × 100

Page 15: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Relative Frequency and Percentage

Distributions

Page 16: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

GRAPHING QUANTITATIVE DATA

How to present quantitative data ??

1- Histograms / a graph in which classes are marked on

horizontal axis and the frequencies are marked on the vertical

axis which represent the height of bars.

In a histogram, the bars are attached to each other.

Page 17: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Histograms

Page 18: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Histograms

What are the shapes of histograms ??

A-) Symmetric histogram / is identical on both sides of its central points.

Page 19: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Histograms

B-) Bimodal symmetric

histogram / is identical on

both sides of its central points

with two modes

Page 20: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Histograms

C-) Uniform or rectangular

histogram ( symmetric ) / the

frequencies of each class are

the same or equal to each other.

Page 21: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Histograms

D-) Skewed to the right

histogram ( positive skewed ) /

Most of data is shown in the

left side of histogram and the

tail on the other right side.

Page 22: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Histograms

E-) Skewed to the left histogram

( negative skewed ) / Most of

data is shown in the right side

of histogram and the tail on the

other left side.

Page 23: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Polygons

2- Polygons / A graph formed by joining the midpoints

of the tops of bars in a histogram with straight lines.

Page 24: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Polygons

Page 25: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Stem and Leaf display

3- Stem and Leaf display / each value is divided into two

portions -- a stem and a leaf. Then the leaves for each stem are

shown separately in a display.

Page 26: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Stem and Leaf display

Construct a stem-and-leaf display for these data

Example / 22 , 26 , 27 , 31 , 33 , 35 , 42 , 44 , 46 , 57 , 58 , 59

, 61 , 63, 64 , 65 ,67

Page 27: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Solution

Page 28: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Reference

• Prem S. Mann 1998, Introductory Statistics, 7th edn, New York, USA.

Page 29: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

Good Luck for All Students

• Please do not hesitate to contact me if you have any questions.

• Dr. Ibrahim AL-Jaafari

• www.Alghamdi-Biostatistics.com

• Email. [email protected]

• Mobile Number : 0553777925

http://www.alghamdi-biostatistics.com/
mailto:[email protected]
Page 30: Lecture 3 Prepared by Dr. Ibrahim AL-Jaafari Lecture 3-4.pdfupper limit of one class and the lower limit of the next class. Class Boundary ... 5–9, 10–14, 15–19, 20–24, and

سبحان هللا وبحمده سبحان هللا العظيم

،، لعل هللا يرحمنا بعلم تعلمناه في الحياة في الوجود ذكر هللا أعظم ما

الدنيا

أستغفر هللا


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