Transcript Measures of central tendency and dispersion

Measures of central tendency
and dispersion
Measures of central tendency
• Mean
• Median
• Mode
• ie finding a ‘typical’
value from the middle
of the data.
You need to be able to:
• Explain how to calculate the mean, median
and mode
• State the strengths and weaknesses of mean,
median and mode
• This could include saying which one you would
use for some data e.g. 2, 2, 3, 2, 3, 2, 3, 2, 97 would you use mean or median here?
Advantages and disadvantages


Mean
More sensitive than the
median, because it makes
use of all the values of the
data.
It can be misrepresentative
if there is an extreme
value.
Median
It is not affected by
It is less sensitive than the
extreme scores, so can give mean, as it does not take
a representative value.
into account all of the
values.
Mode
It is useful when the data
are in categories, such as
the number of babies who
are securely attached.
It is not a useful way of
describing data when there
are several modes.
Measures of Dispersion
• Measures of ‘spread’
• This looks at how
‘spread out’ the data
are.
• Are the scores similar to
each other (closely
clustered), or quite
spread out?
Range and standard deviation
• The range is the difference between the highest
and lowest numbers. What is the range of …
• 3, 5, 8, 8, 9, 10, 12, 12, 13, 15
• Mean = 9.5
range = 12 (3 to 15)
• 1, 5, 8, 8, 9, 10, 12, 12, 13, 17
• Mean = 9.5
range = 16 (1 to 17)
•
Example from Cara Flanagan, Research Methods for AQA A Psychology (2005) Nelson Thornes p 15
Standard deviation
• Standard deviation tells
us the average distance
of each score from the
mean.
• 68% of normally
distributed data is
within 1 sd each side of
the mean
• 95% within 2 sd
• Almost all is within 3 sd
Example
• Mean IQ = 100, sd = 15
• What is the IQ of 68% of
population (ie what is the
range of possible IQs)?
• Between what IQ scores
would 95% of people be?
• Dan says he has done an
online IQ test, and he has
an IQ of 170. Should you
believe him? Why/not?
Another example
• Sol scores 61% in the
test. His mum says
that’s rubbish. Sol
points out that the
mean score in class was
50%, with an sd of 5.
Did he do well?
• What if the sd was only
2?
• What if sd was 15?
Advantages and disadvantages
Advantages
Disadvantages
Range
Quick and easy to calculate
Affected by extreme values
(outliers)
Does not take into account
all the values
Standard deviation
More precise measure of
dispersion because all
values are taken into
account
Much harder to calculate
than the range
I used Cara Flanagan’s (2005) Research Methods for AQA A Psychology Nelson Thornes in preparing these slides.