How To Interpret Frequency Data

Statistical Language - Frequency Distribution

Frequency Distribution

What is a frequency distribution?

Frequency distributions are visual displays that organise and present frequency counts so that the information tin exist interpreted more hands.

Frequency distributions tin show absolute frequencies or relative frequencies, such as proportions or percentages.

How do nosotros show a frequency distribution?

A frequency distribution of information can be shown in a tabular array or graph. Some common methods of showing frequency distributions include frequency tables, histograms or bar charts.

Frequency Tables

A frequency tabular array is a simple way to display the number of occurrences of a detail value or characteristic. For example, if nosotros have collected data about height from a sample of 50 children, nosotros could present our findings as:

Height of Children

Elevation (cm) of children	Absolute frequency	Relative frequency
120 – less than 130	9	18%
130 – less than 140	ten	20%
140 – less than 150	xiii	26%
150 – less than 160	11	22%
160 – less than 170	7	14%
Total	50	100%

From this frequency table we tin quickly identify information such as seven children (fourteen% of all children) are in the 160 to less than 170 cm pinnacle range, and that in that location are more than children with heights in the 140 to less than 150 cm range (26% of all children) than any other meridian range. Data tin also be presented in graphical form.

Frequency Graphs

Histograms and bar charts are both visual displays of frequencies using columns plotted on a graph. The Y-axis (vertical axis) mostly represents the frequency count, while the Ten-centrality (horizontal axis) generally represents the variable existence measured.

A histogram is a type of graph in which each cavalcade represents a

numeric variable, in particular that which is continuous and/or grouped. A histogram shows the distribution of all observations in a quantitative dataset. It is useful for describing the shape, center and spread to better understand the distribution of the dataset. Features of a histogram:

The height of the column shows the frequency for a specific range of values.

Columns are usually of equal width, nevertheless a histogram may bear witness data using unequal ranges (intervals) and therefore accept columns of diff width.

The values represented by each column must be mutually exclusive and exhaustive. Therefore, at that place are no spaces between columns and each observation can only ever vest in one column.

It is of import that at that place is no ambiguity in the labelling of the intervals on the x-centrality for continuous or grouped data (e.g. 0 to less than 10, 10 to less than 20, xx to less than 30). For instance:
The histogram beneath shows the same information equally the frequency table.

Distribution of Children's Height

A bar chart is a blazon of graph in which each column (plotted either vertically or horizontally) represents a categorical variable or a discrete ungrouped numeric variable. It is used to compare the frequency (count) for a category or characteristic with another category or characteristic. Features of a bar chart:

In a bar chart, the bar height (if vertical) or length (if horizontal) shows the frequency for each category or feature.

The distribution of the dataset is not important considering the columns each represent an individual category or characteristic rather than intervals for a continuous measurement. Therefore, gaps are included between each bar and each bar tin be arranged in any order without affecting the data. For example:
If data had been collected for 'land of birth' from a sample of children, a bar nautical chart could be used to plot the information equally 'country of nascence' is a categorical variable.

Birthplace of Children

Country of Birth	Accented frequency	Relative frequency
Australia	16	32%
Fiji	3	half dozen%
India	8	xvi%
Italian republic	10	xx%
New Zealand	9	18%
Us	four	eight%
Total	l	100%

The bar nautical chart below shows u.s.a. that 'Australia' is the most ordinarily observed country of birth of the 50 children sampled, while 'Republic of the fiji islands' is the least mutual country of birth.

Birthplace of Children