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One-variable Data Analysis

Dotplot and Bar graph

Introduction: We have various types of methods for organizing data as well as for arranging data. In order to see patterns and shapes and for presenting an immediate impression of everything about the data, graphical displays are very useful. Generally, we are use Dot plots, Bar charts, Histograms and Stemplots for representing the data because all the graphical displays should be clearly labeled, leaving no doubt what the picture represents.

Dotplot: A dotplot is used to illustrate categorical data [i.e., the data which can be classified into a group]. It is a very simple type of graph that represents the data values with dots, above the corresponding values on a number line.

Bar graph: A bar graph is used to illustrate qualitative data [i.e., categorical data]. It is a common visual display to compare the frequencies of categories or groups. The horizontal axis in bar graph contains categories and the vertical axis in the bar graph contains frequencies (or) relative frequencies. It is used in agricultural, sports, commercial and scientific data.

  • Example: The Centers for Disease Control and Prevention lists leading causes of death in females in the United States during 2009.
    Cause of Death Percent
    Cancer 34.6
    Heart disease 14.4
    Stroke 3.8
    Other 47.2
    The above given data can be displayed in the following bar chart (or) bar graph.
    The relative frequencies of different results are indicated by the heights of the bars representing these results.
Histogram and Stemplot

Histogram: A histogram is used to describe quantitative data. It is composed of bars of equal widths and variable lengths. The horizontal axis in histogram contains numerical values and the vertical axis in the histogram contains frequencies (or) relative frequencies of the values (often intervals of values). It is used in industry, commerce, physics and education sector. It is also used in calculating mode of a frequency distribution.

  • Example: Here are the magnitudes (on the Richter scale) of the 1264 earth-quakes in the National Geophysical Data Center (NGDC) data:

    Like a bar graph, a histogram plots the bin counts as the heights of bars. In this histogram of earthquake magnitudes, each bin has a width of 0.2, so, for example, the height of the tallest bar says that there were about 235 earthquakes with magnitudes between 7.0 and 7.2. In this way, the histogram displays the entire distribution of earthquake magnitudes.

Stemplot (or) Stem and Leaf display: Histograms provide an easy to understand summary of the distribution of a quantitative variable but it doesn't show the data value itself. Stem and leaf display is like a histogram, but it shows the individual values.

Stemplot is little bit complicated than dotplot. Each data value has a stem and a leaf. There are no mathematical rules for what constitutes the stem and what constitutes the leaf. With the given score data, we might choose first digit as stem and second digit as leaf. So the number 54 in a stem and leaf plot would show up as 5 | 4. All the leaves for a common stem are often on the same line and listed in increasing order.

Pie Chart or Circle Graph

Statistical data can also be presented in the form of a pie chart (or circle graph). It shows the relationship between a whole and its part. Here, a circle is divided into various sectors, in proportion with the various component parts of the total.

The following pie chart represents the expenditure (in percentage) on various items and savings of a family during a month.

Steps for the construction of a pie chart
Step 1: Take the total value of all the items equal to 360°.
Step 2: Convert all components of the data into degrees using the following formula:
Degree of any component =
Step 3: Draw a circle of appropriate radius.
Step 4: Draw any radius (preferable horizontal). With this radius as base line, draw an angle at the center equal to the degree represented by the first component. This angular ray will touch the circumference of the circle. In the same way, construct a second sector and other sectors one after the other using the same procedure.
Step 5: Different sectors representing various component parts should be distinguished from one another by using different shades.
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