Key Points

Data is a collection of facts, numbers, measurements, or observations gathered to convey information. For example, the list of heights of students in a class is data.

Tally marks are used for counting frequency. A single vertical line | is one count, and a group of five is represented by NN. For example, a frequency of 8 is written as NN |||.

Frequency is the number of times a particular item or observation occurs in a given dataset. A frequency distribution table lists items and their corresponding frequencies.

A pictograph represents data using pictures or symbols. It is a visual way to compare data, but requires a key to understand the value of each symbol.

The key or scale in a pictograph explains what each symbol represents. For example, a key might state that one symbol \odot equals 10 books.

To find the value for a category in a pictograph, count the number of symbols and multiply by the value given in the key. For example, if \odot = 10 books, then \odot \odot \odot represents $3 \times 10 = 30$ books.

A bar graph, or bar chart, displays data using rectangular bars of uniform width. The length or height of each bar corresponds to the frequency of the data item.

A proper bar graph includes a title, labeled horizontal (x-axis) and vertical (y-axis) axes, and a chosen scale. The bars must have equal width and equal spacing between them.

A scale is chosen for the axis representing frequency to fit the graph on paper. For example, 1 unit of length on the axis can represent 5 students, 10 cars, or 100 runs.

Bar graphs allow for quick comparison of data. The longest bar represents the item with the highest frequency, and the shortest bar represents the item with the lowest frequency.

To draw a bar graph, first draw and label the two axes. Choose an appropriate scale for the frequency axis, then draw bars of correct height or length for each category, keeping width and spacing uniform.

Bar graphs with vertical bars are also called column graphs and are suitable for representing things like height. Horizontal bar graphs are often used for representing things like distance or length.