Graphical Desc
Graphical Techniques to describe a set of Interval data ( cross-sectional data )
A. Histogram ~ A histogram is created by drawing rectangles whose bases are the class intervals (classes) and and whose heights are the frequencies. Determining number of class intervals No. of Observations No. of Classes 50,000 17 - 20
~ Alternatively using Sturges's formula No. of class intervals = 1 + 3.3 log(n) where n = No. of observations ~ Determining class interval widths Class width = (Largest Observation – Smallest Observation ) / No. of Classes ~ Shapes of histogram – based on following characteristics 1. Symmetry – the two sides are identical in shape and size with respect to a vertical line drawn down the center of the histogram 2. Skewness – with a long tail extending to either the right (positively skewed) or the left (negatively skewed) 3. Number of Modal Classes – (A modal class is the class with the largest number of observations) - A unimodal histogram is one with single peak. A bimodal histogram is one with two peaks, not necessarily equal in height 4. Bell shape – A special type of symmetric unimodal histogram. B. Stem-and-leaf Display ~ One of the drawback of the histogram is that we lose potentially useful information by classifying the observations. Stem-and-Leaf method developed by statistician John Tukey overcomes this loss to some extent. The advantage of stem-and-leaf display over histogram is that we can see the actual observations. C. Ogive ~ It is graphical representation of the cumulative relative frequencies. Factors that identify when to use a Histogram, Stem-and-Leaf display, or Ogive 1. Objective – Describe a single set of data 2. Data Type – Interval
Graphical Techniques to describe Time series Data
Line Chart ~ It is a plot of the variable over time. It is created by plotting the variable on the vertical axis and the time periods on the horizontal axis.
Describing the relationship between two interval variables
~ Scatter diagram –
A. Histogram ~ A histogram is created by drawing rectangles whose bases are the class intervals (classes) and and whose heights are the frequencies. Determining number of class intervals No. of Observations No. of Classes 50,000 17 - 20
~ Alternatively using Sturges's formula No. of class intervals = 1 + 3.3 log(n) where n = No. of observations ~ Determining class interval widths Class width = (Largest Observation – Smallest Observation ) / No. of Classes ~ Shapes of histogram – based on following characteristics 1. Symmetry – the two sides are identical in shape and size with respect to a vertical line drawn down the center of the histogram 2. Skewness – with a long tail extending to either the right (positively skewed) or the left (negatively skewed) 3. Number of Modal Classes – (A modal class is the class with the largest number of observations) - A unimodal histogram is one with single peak. A bimodal histogram is one with two peaks, not necessarily equal in height 4. Bell shape – A special type of symmetric unimodal histogram. B. Stem-and-leaf Display ~ One of the drawback of the histogram is that we lose potentially useful information by classifying the observations. Stem-and-Leaf method developed by statistician John Tukey overcomes this loss to some extent. The advantage of stem-and-leaf display over histogram is that we can see the actual observations. C. Ogive ~ It is graphical representation of the cumulative relative frequencies. Factors that identify when to use a Histogram, Stem-and-Leaf display, or Ogive 1. Objective – Describe a single set of data 2. Data Type – Interval
Graphical Techniques to describe Time series Data
Line Chart ~ It is a plot of the variable over time. It is created by plotting the variable on the vertical axis and the time periods on the horizontal axis.
Describing the relationship between two interval variables
~ Scatter diagram –