Dr. Engr. Sami ur Rahman Data Analysis Lecture 3: Data Distribution Normal Distribution

University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 2 Introductory Statistics  Dispersion  The Normal Distribution Curve  Variability  Calculating a Mean and a Standard Deviation  Interpreting Distributions

University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 3 Dispersion Dispersion – The distribution of values around some central value, such as an average. Distribution of a variable tells us what values & how often (frequency of a variable)

Distribution University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 4 St idage St idAge

Distribution (Frequency) University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 5 St idage St idAge AgeFrequency Mean? Median? Mode?

Histogram University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 6 AgeFrequency

The Normal Distribution Curve It is bell-shaped and symmetrical about the mean The mean, median and mode are equal Mean, Median, Mode It is a function of the mean and the standard deviation University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 7

Examples of Normal Distribution Examples of normal distribution in everyday life many: Height Weight Shoe size Exam marks University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 8

Variation or Spread of Distributions Measures that indicate the spread of scores:  Range  Standard Deviation University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 9

Variation or Spread of Distributions Range  It compares the minimum score with the maximum score  Max score – Min score = Range  It is a crude indication of the spread of the scores because it does not tell us much about the shape of the distribution and how much the scores vary from the mean University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 10

Variation or Spread of Distributions Standard Deviation  It tells us what is happening between the minimum and maximum scores  It tells us how much the scores in the data set vary around the mean University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 11

Calculating Mean and Standard Deviation University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 12

University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 13 Standard deviation(s)  Used as a measure of spread when mean=center  Units of s=same as data units  s always positive  Higher s->more spread  s=0->no spread -> all observations equal  s affected by outliers

University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 14 Standard Deviation A measure of dispersion around the mean, calculated so that approximately 68 percent of the cases will lie within plus or minus one standard deviation from the mean, 95 percent within two, and 99.9 percent within three standard deviations. This is often referred to as the rule When to Use Standard Deviation When you need to determine how much a set of scores vary from each other.

Interpreting Distributions Mean = 50 Std Dev = 15 34% 14% 2% 34% 14% 2% s d scores 50%84%98%100%2%0%16% rank University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 15

Interpreting Distributions University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 16

Interpreting Distributions University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 17

Interpreting Distributions University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 18

University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 19 Example-Do women study more than men?  Variable: minutes studied on a typical weeknight of a first- year university class  Random samples of 30 women and 30 men:  Women:180,120,150, 200, 120,90,120,180,120, 150, 60, 240,180,120,180,180,120, 180, 360, 240, 180, 150, 180, 115,240, 170, 150,180,180,120  Men: 90, 90,150,240,30,0, 120,45,120,60,230,200,30,30, 60, 120, 120, 120, 90, 120, 240, 60, 95, 120,200,75,300, 30, 150,180

University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 20 Thanks for your attention