Download Central Tendency and Variability

Central Tendency and
Variability
Chapter 4
Central Tendency
> Mean: arithmetic average
• Add up all scores, divide by number of
scores
> Median: middle score
> Mode: most common score
Calculating the Mean
> Add up all scores
> Divide by number of scores
X

X 
N
Calculating the Median
> Line up the scores in ascending order
> Find the middle number
• For an odd number of scores, just find the
middle value.
• For an even number of scores, divide
number of scores by two.
• Take the average of the scores around this
position.
Calculating the Mode
> Line up the scores in ascending order.
> Find the most frequent score.
> That’s the Mode!
> Do measures of central tendency
capture the following slide adequately?
Figure 4-4: Bipolar Disorder and the Modal Mood
Outliers and the Mean
> An early lesson in lying with statistics
• Which central tendency is “best”: mean,
median, or mode?
Figure 4-6:
The Mean without the
Outlier
Which Measure of Central
Tendency is the Best?
> The mean is most commonly used –
best for symmetric distributions
> The median is best for a skewed
distribution or one with outlier(s),
> The mode is used in 3 cases:
• One particular score dominates a
distribution
• Distribution is bimodal or multimodal
• Data are nominal
Measures of Variability
> Range
• From the lowest to the highest score
> Variance
• Average square deviation from the mean
> Standard deviation
• Variation from the sample mean
Calculating the Range
> Determine the highest score
> Determine the lowest score
> Subtract the lowest score from the
highest score
Range  xHighest  xLowest  10  1  9
Calculating the Variance
> Subtract the mean from each score
> Square every deviation from the mean
> Sum the squared deviations
> Divide the sum of squares by N
SD
2
(X  M )


N
2
Calculating the Standard
Deviation
> Typical amount the scores vary or
deviate from the sample mean
• This is the square root of variance
SD 
(X  M )
N
2
Practice Problem
> Age of Classmates?
• Calculate the mean, median, mode,
standard deviation, and the variance for
the age of the members of your class.
Interquartile Range
> Measure of the distance between the 1st
and 3rd quartiles.
> 1st quartile: 25th percentile of a data set
> The median marks the 50th percentile of
a data set.
> 3rd quartile: marks the 75th percentile of a
data set
Calculating the Interquartile
Range
Countries’ top finishes in the World Cup omitting
countries with a score of 0
1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 4, 6, 8, 10