e-Statistics
Introduction
  • Advanced User Guide
    Assignment & Quiz
  • User Account
  • Guide to Worksheet 1-2
  • Guide to Worksheet 3-4
  • Guide to Worksheet 5-6
  • Guide to Worksheet 7-8
    Data in Statistical Studies
  • Overview
  • Data from SMDA
  • Data and Story Library
    Exploratory Graphics
  • Overview
  • Histogram
  • Stem and Leaf Plot
  • Boxplot
  • Scatter Plot
  • QQ plot
  • Bar Graph
    Descriptive Statistics
  • Overview
  • Summary Statistics
  • Grouped Data
  • Frequency Table
    Discrete Distributions
  • Frequency Function
  • Binomial Distribution
  • Normal Approximation
    Normal Distribution
  • Normal Density Function
  • Critical Point
  • Z-score
  • Central Limit Theorem
    Inference on Mean
  • t-Distribution
  • Confidence Interval
  • Hypothesis Test
  • Power of Test
  • One-sided CI
    Comparison of Two Groups
  • Overview
  • t-Test
  • Nonparametric Test
  • Test for Paired Data
    Inference on Variances
  • Chi-square Distribution
  • Testing a Standard Deviation
  • F-Distribution
  • F-Test
    Explore Statistics in Drug Safety

    • Histogram

    Histogram uses bars of varying height which are proportional to the number of data within bands. This graphical presentation can be used to describe the characteristics of the data. A histogram with one peak is called unimodal. When the histogram has two major peak, it is said to be bimodal, suggesting a possibility of two distinct populations in the data. A symmetric histogram has two symmetric tails on both side, whereas a skewed histogram has a longer tail on one side than that on the other. We call it right-skewed or left-skewed accordingly as we observe the longer right-hand tail or the longer left-hand tail

    The width of each interval (or band) is called bandwidth. If the bandwidth is too large then the graph fails to convey the structure of the data. On the other hand if it is too small then it becomes too spiky.

    The number of observations within a band is called frequency. Whereas, the relative frequency is calculated by

    $\displaystyle ($relative frequency$\displaystyle ) = \frac{(\mbox{\it frequency})}{(\mbox{\it data size}) \times (\mbox{\it bandwidth})}. $

    When the relative frequency is used for the y-axis (the vertical axis), the area under the histgram between $ a =$ and $ b =$ represents roughly the percentage of the sample distribution. In fact, is the actual percentage of the observed values within the interval $ (a,b]$ . (The interval will be $ [a,b]$ if $ a$ is not greater than the minimum.)