 # Data Analysis and Presentation of Results

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## Data Analysis and Presentation of Results

#### Central tendency and dispersion

Below is a list of terms that are commonly used, it is important to know how to use them:

Arithmetic mean: All values in a set of data are added together and divided by the number of values (N). Used with normal distribution and interval level data. Not suitable for use where extreme values can distort the mean. The most sensitive measure of central tendency.

Median: All values are arranged in order, the middle value is the median. Used with interval or ordinal level data, the median is not affected much by extreme values.

Mode: The most frequent value or score in a set of data. Used with nominal data. Does not give any information about other values.

Range: Simple measure of dispersion- shows the total spread of data. Difference between highest and lowest scores in a set of data: top value minus bottom value plus 1. Affected by atypical, extreme values.

Standard Deviation: Measure of dispersion- shows degree of clustering of values around the mean. Calculating standard deviation (S): Square root of sum of all squared deviations from the mean, divided by N (or sometimes N-1). The most accurate measure of dispersion.

#### Graphs and charts

Graphs and charts give a quick visual impression of any patterns or trends in your results. They should be used to help summarise your results.

You need to remember the difference between a bar chart, a histogram and a frequency polygon.

Bar charts:

Used for nominal data (data in categories).

The x-axis (frequencies are usually on the y-axis) does not need to show a complete scale (if showing categories).

There should be gaps between the bars.

Histograms:

Used for interval or ordinal data.

No intervals (if data is grouped) are missed, even if they are empty. Class intervals are represented by their mid-point at the centre of each column.

There are no gaps between columns.

Frequency polygons:

Used for interval or ordinal data.

All class intervals are represented.

Instead of columns, a line is used to join the mid-point of each class interval.

See how you get on with the exercise below. Drag the three pink boxes onto the correct blue box and then mark your answer:

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