Download descriptive statistics summary

These provide ways in which the researcher can obtain summary descriptions of
sets of quantitative data. 2 types are measures of central tendency, which
give average values, and measures of dispersion, which look at the variability
of scores. These give a single value that summarises a set of data. However,
this also produces a loss of individual information.
Measures of central tendency
These provide a single value that is representative of a set of numbers by
indicating the most typical value.
This is your set of numbers: 4, 6, 7, 3, 6, 2, 8, 1, 9, 5, 6, 2, 3.
Use the information below to complete your notes (p.47,48,49)
Under how to calculate, use these numbers to calculate the relevant value, showing
your workings.
How to calculate
Mean
Median
Mode
This is known as the
statistical average
and all scores are
added up and
divided by the
number of scores
The mean of the set
of data given
is………………..
Scores are put into
rank order, and it is
the central score –
if there is an even
number, the median
is the mid point
between the 2
scores
The median score
from the example
data is…….
The most common
number in a set of
scores
The mode is….
Advantages
Makes use of all the
data and therefore is
the most sensitive
measure of central
tendency
Especially useful if the
scores represent a
normal distribution
Not affected by
extreme scores
Disadvantages
It can be
misrepresentative if there
are extreme values
and therefore this is
misleading.
e.g. if our set of numbers
has 57 in it, the mean is
actually …..
Not useful for small sets
of data especially if these
contain widely varying
scores e.g. 7 8 9 102 121
Not as sensitive as the
mean because not all the
values are not reflected
Useful when the data is
in categories
Not useful when there are
several modes (multimodal)
Does not tell us about the
other values in the
distribution
Measures of dispersion
A single value showing the variation/spread of scores in a set of data.
How to calculate
Range
Standard
deviation
(use this
therefore
when the mean
is used)
The
interquartile
range
This is calculated by taking
away the lowest value from
the highest value in a set of
scores
The range value for the
example data is……..
This is a measure of the
spread or variability of a set
of scores from the mean.
The larger the S.D, the
larger the spread of scores
from the mean and vice versa
Don’t need to calculate
This measures the spread of
the middle 50% of values
when they are placed in
numerical order
Don’t need to calculate!
Advantages
Disadvantages
Easy to calculate
Affected by extreme
values
Gives a basic
measure of the
variation within the
data.
If there are extreme
values therefore it is
inappropriate
It is a sensitive
measure of
dispersion as it takes
all the data into
account
Harder/more timeconsuming to calculate
The top and bottom
25% are ignored,
which removes the
influence of any
outlying values
It is inaccurate if there are
large intervals between the
scores
It is less meaningful if data
aren’t normally distributed
Easy to calculate,
more so than the s.d.
Exam hint: You may be presented with data and then asked
which measure of central tendency/dispersion to use and
have to justify your choice. Justify means give reasons
for, not describe what it is. So, look at the type of data (is
it category-based or not), are there any extreme values?
and does the calculation need to be quick and easy?