Histograms

Relative Frequency Histogram

Has the same shape and horizontal scale as a histogram, but the vertical scale uses relative frequencies (as percentages or proportions) instead of actual frequencies.

Uniform Distribution

The different possible values occur with approximately the same frequency, so the heights of the bars in the histogram are approximately uniform.

Assessing Normality with a Normal Quantile Plot - Normal Distribution

The population distribution is normal if the pattern of the points in the normal quantile plot is reasonably close to a straight line, and the points do not show some systematic pattern that is not a straight-line pattern.

Assessing Normality with a Normal Quantile Plot - Not a Normal Distribution

The population distribution is not normal if the normal quantile plot has either or both of these two conditions: The points do not lie reasonably close to a straight-line pattern. The points show some systematic pattern that is not a straight-line pattern.

Interpreting Histograms - CVDOT

The ultimate objective of histograms is to understand characteristics of the data. Explore the data by analyzing the histogram to see what can be learned about "CVDOT": the center of the data, the variation, the shape of the distribution, whether there are any outliers, and time (change in data over time).

Important Uses of Histograms

Visually displays the shape of the distributions of data. Shows the location of the center of the data. Shows the spread of the data. Identifies outliers.

Normal Distribution

When graphed as a histogram, a normal distribution has a "bell" shape. Many statistical methods require that sample data come from a population having a distribution that is approximately a normal distribution, and we can often use a histogram to judge whether this requirement is satisfied. There are many more advanced and less subjective methods of determining whether the distribution is a normal distribution. Normal quantile plots are very helpful for assessing normality.

Basic Concepts of Histograms

While a frequency distribution is a useful tool for summarizing data and investigating the distribution of data, an even better tool is a histogram, which is a graph that is easier to interpret than a table of numbers.

Skewness

A distribution of data is skewed if it is not symmetric and extends more to one side than to the other. Data skewed to the right (positively skewed) have a longer right tail. Data skewed to the left (negatively skewed) have a longer left tail.

Mnemonic for Skewness

A distribution skewed to the right resembles the toes on your right foot, and one skewed to the left resembles the toes on your left foot. Distributions skewed to the right are more common than those skewed to the left because it's often easier to get exceptionally large values than values that are exceptionally small.

Histogram

A graph consisting of bars of equal width drawn adjacent to each other (unless there are gaps in the data). The horizontal scale represents the classes of quantitative data values, and the vertical scale represents frequencies. The heights of the bars correspond to frequency values.

A Histogram Graphs Frequency Distribution

A histogram is basically a graph of a frequency distribution. Class frequencies should be used for the vertical scale. There is no universal agreement on the procedure for selecting which values are used for the bar locations along the horizontal scale, but it is common to use class boundaries or class midpoints or class limits or something else.