Graphs

• what are the five methods of the presentation and display of quantitative data?

  tables, bar chart, histogram, line graph and scattergram.
• tables


  raw scores displayed in columns and rows

  a summary paragraph beneath the table explains the results.
• bar chart

  categories (discrete data) are usually placed along the x axis and frequency on the y axis (or can be reversed)

  the height of each column represents the frequency of that item.
• histogram


  bars touch each other- data is continuous rather than discrete. there is a true zero.
• line graph


  frequency on one axis, data on the other axis is continuous.

  the line often shows how something changes, e.g. over time.
• scattergram


  used for correlational analysis. each dot represents one pair of related data.

  the data on both axis must be continuous.
• what are the two types of distributions?

  normal and skewed
• normal distributions


  symmetrical, bell-shaped curve. most people are in the middle area of the curve with very few at the extreme ends.

  the mean, median and mode all occupy the same midpoint of the curve.
• skewed distributions.


  distributions that lean to one side or the other because most people are either at the lower or upper end of the distribution.
• what are the two types of skews?

  negative and positive.
• negative skew


  most of the distribution is concentrated to the right of the graph, resulting in a long tail on the left.

  e.g. a very easy test which most people get high marks would produce a negative skew.

  the mode is the highest point of the peak, the median comes next to the left, and the mean is dragged across to the left (if scores are arranged from lowest to highest).
• positive skew


  most of the distribution is concentrated towards the left of the graph, resulting in a long tail on the right.

  e.g. a very difficult test in which most people get low marks would produce a positive skew.

  the mode is the highest point of the peak, the median comes next to the right, and the mean is dragged across to the right (if scores are arranged from lowest to highest).