EDEXCEL GCSE HIGHER MATHS - What are Frequency Tables, Histograms, and Box Plots

Frequency Tables, Histograms, and Box Plots

Frequency Tables

A frequency table is a way of organising data by showing how often each value appears in a data set.

Example:

Let's say we have the following data set:

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5

We can create a frequency table for this data:

Key Points:

• The frequency is the number of times a value appears in the data set.
• The total frequency is the sum of all frequencies.
• Frequency tables can be used to visualise data and to calculate measures of central tendency and spread.

Histograms

A histogram is a bar chart that shows the frequency distribution of a data set.

Key Features:

• Bars are adjacent: The bars touch each other to show the continuous nature of the data.
• Area of each bar represents frequency: The area of each bar is proportional to the frequency of the corresponding class interval.
• Horizontal axis represents the data values: The horizontal axis is typically divided into class intervals, which represent ranges of data values.
• Vertical axis represents the frequency: The vertical axis represents the number of occurrences of each value or range of values.

Example:

The following histogram represents the frequency distribution of the data set shown in the frequency table example above:

     *
   ***
 *****
 *******
 *****
 ***
 *

 1 2 3 4 5

Key Points:

• Histograms are useful for visualising the shape and distribution of data.
• They can be used to identify patterns, such as skewness and outliers.

Box Plots

A box plot is a graphical representation of a data set that shows the minimum, maximum, median, first quartile (Q1), and third quartile (Q3).

Key Features:

• Box: The box represents the interquartile range (IQR), which is the range between Q1 and Q3.
• Median: The vertical line inside the box represents the median.
• Whiskers: The lines extending from the box represent the range of the data, excluding outliers.
• Outliers: Any data points that lie outside the whiskers are considered outliers and are plotted individually.

Example:

The following box plot represents the same data set as the frequency table and histogram examples above:

    *
   |  *
  +---+
  |   |
  +---+
   |   *
    *

  1  2  3  4  5

Key Points:

• Box plots are a good way to compare the distribution of two or more data sets.
• They can be used to identify the spread, skewness, and outliers of a data set.

In conclusion, frequency tables, histograms, and box plots are powerful tools for visualising and analysing data. They can be used to identify patterns, trends, and outliers in data sets, making them essential tools for data interpretation.