Measure of Spread - Data Analysis in Psychology - Lecture Slides, Slides of Advanced Data Analysis

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Measures of Spread

1. Range: the distance from the lowest to the highest score

• Problem of clustering differences

** Problem of outliers

2. Interquartile Range

• omits the upper and lower 25% of scores
• eliminates the effect of extreme scores
• trimmed samples
• loss of information

Data Set I:

8, 8, 9, 10, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 14,14, 15, 15, 16, 17

Range = 9 Interquartile Range = 3

Data Set II:

1, 2, 3, 10, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 14,14, 15, 21, 25, 30

Range = 29 Interquartile Range = 3

Variance:

Standard

Deviation:

These are here defined as descriptive statistics.

average of the summed, squared-deviations about the mean

n

y y

s y

2 2

the square root of the average of the summed squared deviations about the mean

n

y y

s y^ ∑^

2

As inferential statistics

2 2

n

y y

s y

2

= ∑^

n

y y

s y

See the difference