Lesson 14 Mathematical Concepts and distributions

Question 1

Tables

Answer 1

When tables appear in the results section of a research report they are not raw scores but have been converted to descriptive statistics (measures of central tendency or dispersion). There should be a paragraph beneath the table explaining the data.

Question 2

Graphs

Answer 2

All four types of graphs you need to know about are drawn with two axis, the vertical axis is the y-axis and the horizontal axis is the x-axis.

Please remember that you should have a title and also label both the x and y axis.

Question 3

Bar charts

Answer 3

These are used for nominal data. The height of each bar represents the frequency of each item. In a bar chart a space is left between each bar to indicate the lack of continuity. The frequency of each category is plotted on the vertical y-axis.

Question 4

Histograms

Answer 4

These are used for ordinal or interval data. It is similar to a bar chart except that the area within the bars must be proportional to the frequencies represented. In practice this means that the y-axis must start at zero. There should be no gaps between the bars.

Question 5

Line Graphs

Answer 5

There are represent ordinal or interval data. They use points connected by lines to show how something changes in value, for instance, over time. Typically, the independent variable (IV) is plotted on the x-axis and the DV on the y-axis.

Question 6

Scattergrams / Scatter graphs

Answer 6

They do not depict differences, but relationships between co-variables (correlations). Either of the co-variables occupies the x-axis and the other the y-axis. Each point on the graph corresponds to the x and y position of the co-variables. The closer the points on the graph are to a straight line the stronger the correlation.

Question 7

Distributions

Answer 7

With most data sets the frequency of these measurements should reflect a bell shaped curve. This is called a normal distribution curve which is symmetrical. Within a normal distribution most people are located in the middle area of the curve and very few people are at extreme ends. The mean, mode and median all occupy the same mid-point of the curve. The ends of the curve never touch the horizontal x-axis (and therefore never reach 0) as more extreme scores are always theoretically possible.

Not all distributions form such a balanced symmetrical pattern. Some data sets derived from psychological scales or measurements may produce skewed distributions, this is when distributions appear to lean to one side.

A positive skew is where most of the data is concentrated to the left of the graph. In this case the mode remains at the highest point of the peak, the median comes next but the mean has been dragged across to the right.

The opposite occurs in a negative skew.