Research

histogram

A histogram is one of the basic quality tools. It is used to graphically summarize and display the distribution and variation of a process data set. A Histogram is a graphical display of data using bars of different heights. A frequency distribution shows how often each different value in a set of data occurs. A histogram is a specialized type of bar chart. Individual data points are grouped together in classes, so that you can get an idea of how frequently data in each class occur in the data set. High bars indicate more points in a class, and low bars indicate less points

Bi-Modal (double-peaked)

• Distribution appears to have two peaks • May indicate that data from more than one process are mixed together • A bi-modal curve often means that the data actually reflects two distinct processes with different centers. You will need to distinguish between the two processes to get a clear view of what is really happening in either individual process

shape of data

skewness and Kurtosis (normal distribution or not) many distributions are not normal.

leaf

the units place ex: in the numbers 92 & 93 ..2&3 are the leafs

what questions can a histogram help you answer?

• What is the most common system response? • What distribution (center, variation and shape) does the data have? • Do the data look symmetric or are they skewed to the left or right?

skewed distribution

A "skewed" distribution is one that is not symmetrical, but rather has a long tail in one direction. If the tail extends to the right, the curve is said to be right-skewed, or positively skewed. If the tail extends to the left, it is negatively skewed. Skewness refers to the degree of asymmetry of a distribution.

Stem and Leaf Plots

A Stem and Leaf Plot is a type of graph that is similar to a histogram but shows more information. The Stem-and-Leaf Plot summarizes the shape of a set of data (the distribution) and provides extra detail regarding individual values.

negatively skewed distribution

A negatively skewed distribution has a long tail in the negative direction (long left tail). It is sometimes called skewed to the left." It is characterized by many small gains and a few extreme losses. For the negatively skewed distribution, the mean is less than the median, which is less than the mode. In this case, there are large, negative outliers which tend to "pull" the mean downward.

positively skewed distribution

A positively skewed distribution means that it has a long tail in the positive direction (a long right tail). It is sometimes called "skewed to the right". It is characterized by many small losses and a few extreme gains. For the positively skewed distribution, the mode is less than the median, which is less than the mean.

univariate data displayed as

For univariate data most common and useful graphs are: Histograms Bar-graphs Stem-and-leaf plots Box plots

STATISTICAL GRAPHICS

Graphical method for analyzing data

histograms are great to show

Histograms are a great way to show results of CONTINUOUS data, such as: height, weight, how much time etc

normal distribution

If a distribution is symmetrical, each side of the distribution is a mirror image of the other. For a symmetrical, bell-shaped distribution (known as the normal distribution), the mean, median and mode of the distribution are equal.

why would skewness occur?

It occurs due to the existence of extremely large or small values in the data set. It allows us to see if large positive or negative deviations dominate

Kurtosis

Kurtosis is also a measure of the length of the tails of a distribution. For example, a symmetrical distribution with positive kurtosis indicates a greater than normal proportion of product in the tails. Negative kurtosis indicates shorter tails than a normal distribution would have.

abnormal distribution

Skewness appears as an uneven curve (with one tail longer than the other); values taper to one side.

how are stem and leaf plots organized?

The data are arranged by place value. The digits in the largest place are referred to as the stem The digits in the smallest place are referred to as the leaf (leaves). The leaves are always displayed to the left of the stem. Stem and Leaf Plots are great organizers for large amounts of information.

what are graphs useful for?

Useful for analyzing information from univariate data as well as bivariate

goal of statistical graphics

Visually communicate information Record data in a compact fashion Visually analyze data to learn more about its structure

if your data is in categories, you should use a

bar chart

stem

digits in the tens place ex in the numbers 92&93...9 is the stem