Graphical representations in statistics provide a visual method for understanding and interpreting complex data sets. This guide focuses on four key graphical techniques: stem-and-leaf diagrams, box-and-whisker plots, histograms, and cumulative frequency graphs.

Stem-and-Leaf Diagrams

Quick Guide:

• Stems: Use the first digits of your numbers.
• Leaves: Use the last digit of each number.
• Order: Arrange numbers in ascending order, align leaves with stems.
• For Comparison: Use back-to-back format for two data sets.

Example:

Data sets A [12, 14, 22, 23, 27], B [15, 19, 20, 26, 28].

• Stems: 1 and 2 (for tens digit).
• Leaves for A: 2, 4 (stem 1), 2, 3, 7 (stem 2).
• Leaves for B: 5, 9 (stem 1), 0, 6, 8 (stem 2).
• Diagram: Write stems in the middle, A's leaves on left, B's on right.

Illustration:

Box-and-Whisker Plot

Quick Guide:

• Order Data: Arrange from smallest to largest.
• Median (Q2): Middle value.
• Lower (Q1) and Upper Quartiles (Q3): Medians of lower and upper halves.
• Min/Max Values: Smallest and largest numbers.
• Draw Plot: Box from Q1 to Q3, line at Q2, whiskers to Min and Max.

Example:

Data [10, 13, 15, 18, 20, 22, 25, 30, 35].

• Median (Q2): 20.
• Q1: (13+15)/2 = 14.
• Q3: (25+30)/2 = 27.5.
• Min/Max: 10, 35.

Illustration:

Histogram

Quick Guide:

• Bins: Decide intervals.
• Frequency: Count numbers in each bin.
• Draw Histogram: Bins on x-axis, frequency on y-axis.

Example:

Data [2, 3, 3, 4, 5, 6, 7, 8, 9].

• Bins: 2-4, 5-7, 8-9.
• Frequencies: Bin 2-4 has 4 values, 5-7 has 3, 8-9 has 2.

Illustration:

Cumulative Frequency Graph

Quick Guide:

• Cumulative Frequency: Add each number to the sum of previous numbers.
• Plot: x-axis for values, y-axis for cumulative frequencies.

Example:

Data [5, 10, 15, 20, 25].

• Cumulative Frequencies: 1, 2, 3, 4, 5.
• Plot Points: (5, 1), (10, 2), (15, 3), (20, 4), (25, 5).

Illustration: