histogram

Examples of histogram in the following topics:

• Recognizing and Using a Histogram

  • A histogram is a graphical representation of the distribution of data.
  • A histogram is a graphical representation of the distribution of data.
  • A histogram has both a horizontal axis and a vertical axis.
  • An advantage of a histogram is that it can readily display large data sets (a rule of thumb is to use a histogram when the data set consists of 100 values or more).
  • A histogram may also be normalized displaying relative frequencies.

• Conclusion

  • It is often useful to display the data collected in an experiment in the form of a histogram.
  • Probability histograms are similar to relative frequency histograms in that the Y-axis is labeled with probabilities, but there are some differences to be noted.
  • The above example of a probability histogram is an example of one that is normal.
  • The most obvious way is to look at the histogram itself.
  • Explain how a probability histogram is used to normality of data

• Optional Collaborative Exercise

  • As a class, construct a histogram displaying the data.
  • Discuss, also, the shape of the histogram.

• Probability Histograms

  • A probability histogram is a graph that shows the probability of each outcome on the $y$-axis.
  • A histogram is particularly useful when there is a large number of observations.
  • Regular histograms have a $y$-axis that is labeled with frequency.
  • Probability histograms are similar to relative frequency histograms in that the $y$-axis is labeled with probabilities, but there are some difference to be noted.
  • Explain the significance of a histogram as a graphical representation of data distribution

• From histograms to continuous distributions

  • Examine the transition from a boxy hollow histogram in the top-left of Figure 2.26 to the much smoother plot in the lower-right.
  • In this last plot, the bins are so slim that the hollow histogram is starting to resemble a smooth curve.
  • This smooth curve represents a probability density function (also called a density or distribution), and such a curve is shown in Figure 2.28 overlaid on a histogram of the sample.

• Histograms

  • A histogram is a graphical method for displaying the shape of a distribution.
  • In a histogram, the class frequencies are represented by bars.
  • A histogram of these data is shown in Figure 1.
  • Histograms can be based on relative frequencies instead of actual frequencies.
  • In the end, we compromised and chose 13 intervals for Figure 1 to create a histogram that seemed clearest.

• The Density Scale

  • Histograms are used to plot the density of data, and are often a useful tool for density estimation.
  • To see this, we compare the construction of histogram and kernel density estimators using these 6 data points:
  • For the histogram, first the horizontal axis is divided into sub-intervals, or bins, which cover the range of the data.
  • Comparison of the histogram (left) and kernel density estimate (right) constructed using the same data.
  • Describe how density estimation is used as a tool in the construction of a histogram.

• Guidelines for Plotting Frequency Distributions

  • These frequencies are often graphically represented in histograms.
  • The total area of the histogram is equal to the number of data.
  • An example of the frequency distribution of letters of the alphabet in the English language is shown in the histogram in .
  • A histogram may also be normalized displaying relative frequencies.
  • The rectangles of a histogram are drawn so that they touch each other to indicate that the original variable is continuous.

• Probability Histograms and the Normal Curve

  • If you were to construct a probability histogram of these events with many trials, the histogram would appear to be bell-shaped.
  • The most obvious way is to look at the histogram itself.
  • This is a sample of size 50 from a right-skewed distribution, plotted as a histogram.
  • This is a sample of size 50 from a normal distribution, plotted out as a histogram.
  • The histogram looks somewhat bell-shaped, indicating normality.

• Graphing Quantitative Variables

  • The upcoming sections cover the following types of graphs: (1) stem and leaf displays, (2) histograms, (3) frequency polygons, (4) box plots, (5) bar charts, (6) line graphs, (7) scatter plots, and (8) dot plots.
  • Some graph types such as stem and leaf displays are best-suited for small to moderate amounts of data, whereas others such as histograms are best-suited for large amounts of data.