Data Displays

A line graph is used to show how a set of data changes with respect to another quantity, often a period of time. To make a line graph, a scale and intervals for the coordinate axes are chosen. The data points are then graphed and a line connecting the points drawn. Consider a table of values that represents the growth of a plant over several weeks.

	Plant Growth
Week	1	2	3	4	5
Height (in.)	1.5	2.3	4	6.2	8

The height data includes values from 1.5 to 8, so a scale from 0 to 10 inches with an interval of 1 inch is reasonable. The horizontal axis can represent time in weeks and the vertical axis can represent the plant height in inches. Now the points can be plotted on a coordinate plane and connected with a line.

By observing the upward and downward slant of the lines connecting the points, the trends in the data can be described and future events can be predicted.

A dot plot, also known as a line plot, is a way to represent numerical or categorical data in which each data point is represented with a dot above a horizontal line with numbers or categories. Dots representing the same measurement are stacked above each other. Consider the following data set. { 4, 4, 3, 1, 4, 4, 1, 4 }

• There are two 1s in this data set, so two dots are stacked above the number 1 on the number line of the corresponding dot plot.
• There is one 3 in this data set, so a single dot is drawn above number 3.
• There are five 4s in this data set, so five dots are stacked above number 4 on the number line.

Dot plots are normally used for discrete data. For data sets containing more than 20 data points, dot plots are often inconvenient and other representations are preferred.

A box plot, or box and whisker plot, can be used to illustrate the distribution of a data set. A box plot has three parts.

• A rectangular box that extends from the first to the third quartiles (Q_1 and Q_3) with a line between Q_1 and Q_3 indicating the position of the median.
• A segment attached to the left of the box that extends from the first quartile to the minimum of the data set.
• A segment attached to the right of the box that extends from the third quartile to the maximum of the data set. The two segments are called whiskers.

If a data set has outliers, they are marked as separate points to the left and/or right of the whiskers. A box plot is a scaled figure and is usually presented above a number line. The set of numbers used to draw the box plot is called the five-number summary of the data set. Each of the five numbers is labeled below.

A box plot provides a visual illustration of the distribution of a data set. Each segment of the plot contains one quarter, or 25 %, of the data, and the center 50 % of the data lies inside the box. The further apart the segments are, the greater the spread is for that quarter of the data.

A histogram is a graphical illustration of a frequency distribution of a data set that contains numerical data. Histograms have several defining characteristics.

• The data is grouped into specific ranges of values known as intervals.
• All intervals in a histogram must be the same size.
• Interval data is marked in groups along the horizontal axis.
• A histogram is a collection of rectangles drawn above the intervals.
• The height of each rectangle is proportional to the frequency of the data in the corresponding interval.

Consider an example situation. A grocery store wants to examine the weights of the apples they sell. To read the distribution, it is not necessary to show each apple's weight individually. Instead, the apples can be grouped by their weights in intervals of 10 grams: 70 -- 79g, 80 -- 89g, and so on. A histogram looks similar to a bar graph. The difference is that a histogram always has intervals of numbers on the horizontal axis and the bars cannot have a space between each other because the data is continuous.

A bar graph is a graphical representation of a categorical data. It is made of rectangular bars and each bar represents a category and its corresponding value. Bar graphs are commonly used to show frequency distributions, in which case they are often created using the data in a frequency table.

A bar graph can be oriented either horizontally or vertically by swapping which axis shows the categories and which shows the value of each category. For example, consider a group of students who are asked what their favorite color is. The categories and values will be adjusted accordingly. The graphical representation of a frequency distribution for numerical data is called a histogram.

A pie chart is a circular chart used to represent the relative frequencies of a data set. It is also called a circle chart. These charts are divided into several slices — each representing a group of the whole data set. The following characteristics are typical of pie charts.

• Each slice is drawn using a different color to differentiate the groups.
• The central angle of each group, as well as its area, is proportional to its relative frequency.

A pie chart allows the visualization of each individual data group when compared to the whole. Alone, however, the chart does not give information about the frequency of each group.

Pie charts might also include the relative frequency of each group written as a percentage. It is also possible to include labels to represent each group with matching colors.

A scatter plot is a graph that shows each observation of a bivariate data set as an ordered pair in a coordinate plane. Consider the following example, where a scatter plot illustrates the results gathered at a local ice cream parlor. This study records the number of ice creams sold and the corresponding air temperature.

Among other insights, the graph shows that when the temperature is about 100^(∘)F, approximately 4000 ice creams are sold. Additionally, as the temperature increased, the number of sales also increased. In this case, it can be said that there is a positive correlation between the variables of the data set — the number of ice creams sold and the air temperature.

A stem-and-leaf plot is a table that orders numerical data, which can be either discrete or continuous, and shows how they are distributed. A stem-and-leaf plot is constructed by breaking each number from the data into a stem and a leaf. The stem of the number is all but the last digit and the leaf is always the last digit. Stem-and-leaf plots include a key that defines how the numbers in the set are to be interpreted.

Examples

The following stem-and-leaf plot represents the set of numbers 5, 7, 10, 11, 12, 14, 23, 23, 27, 38, 40, and 41. Since 23 appears in the data set twice, the number 3 will appear twice in the leaf of the 2 line. r|cccc 0 & 5 & 7 1 & 0 & 1 & 2 & 4 2 & 3 & 3 & 7 3 & 8 4 & 0 & 1 Key: 4|1 means 41 Here is a stem-and-leaf plot representing the numbers 95.1, 95.2, 95.5, 96.0, 96.4, 96.6, 98.1, and 98.7. The decimal point does not need to be included in the plot as it can be concluded from the key where it should be placed. r|ccc 95 & 1 & 2 & 5 96 & 0 & 4 & 6 97 98 & 1 & 7 Key: 95|1 means 95.1

Note how the leaf part of the table is left empty when the stem is 97. Since the role of the plot is to also show how the data is distributed, empty rows should not be omitted.