Measures of Central Tendency
Aim to identify the average/most typical value in a dataset
The mean, median, and mode
Mean
The average value of a dataset. ‘x̄’
Mean STRENGTHS/WEAKNESSES
S: Highly sensitive; takes ALL values into account
W:Affected by extreme values/outliers, skewing distribution
What type of data is mean used for?
Interval/Ratio Data
Median
The middle value of a dataset when put into numerical order from smallest–>largest
Median STRENGTHS/WEAKNESSES
S: Unaffected by extreme values/outliers
W: Doesn’t take all values into account; not Sensitive
What type of data is median used for?
Ordinal Data (commonly)
Mode
The most common value found in a dataset
-If there are 2, then it is known as being bimodal
Mode STRENGTHS/WEAKNESSES
S:Unaffected by extreme values/outliers + Easy to calculate
W:Doesn’t take all values into account, Not useful for small datasets/those with multiple modes
What type of data is mode used for?
Nominal data (commonly)
Frequency Tables
Shows how many times a value occurs in a dataset
-Can observe theems/differences
Measures of dispersion
Descriptive statistics that aim to identify the spread of scores within a dataset from the measures of central tendency; how VARIED the scores are
Range
Explains the range between largest and smallest scores, indicating how spread out the data is
Range STRENGTHS/WEAKNESSES
-Easy to calculate (largest value-smallest)
-Affected by extreme scores, so not appropriate for datasets containing outliers
-Doesn’t explain whether scores are bunched or spread around the mean
Standard Deviation
Tells the average amount by which each score ‘deviates’ from the mean
Standard Deviation STRENGTHS/WEAKNESSES
-Takes all values into account; more precise and sensitive
Standard Deviation Equation
Bar Charts
-Use nominal data (distinct, operate categories; equal gaps MUST be drawn between bars)
- x-axis labelled with categories of data
Histograms
-Use interval/ratio data (continuous scale; NO gaps drawn)
- x-axis labelled with the scale/range of data
Distribution (DEFINITION)
Describes how the data is spread out
Normal Distribution
The graph is symmetrical, with mean=median=mode
Positively Skewed Distribution
Data is skewed to the right- long tail to the right
Mode<Median<Mean
Negatively Skewed Distribution
Data is skewed to the left- long tail to the left
Mode>Median>Mean
Low SD indicates…
Consistency in scores. all bunched close together around the mean