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Transcript
POPULATION
MEASURES
Mean, Median and Mode
Quartiles and Standard Deviation
Measures of Central Tendency
• The average of a set of data can be quoted at the mean,
median or mode.
• In different situations it is more appropriate to choose one
of these over the other two.
• Mean =
𝑠𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑖𝑒𝑐𝑒𝑠 𝑜𝑓 𝑑𝑎𝑡𝑎
• Median = middle number when the data is ranked in order
• Mode = the number that occurs most often
The mean
• If the results are symmetrical and continuous then can
legitimately use the mean.
• The main disadvantage with the mean is that it includes
every piece of data. This can be a problem when you
have especially large/small outliers in the data set.
The Median
• The median is usually preferred when the data set is
skewed or you are dealing with ordinal data e.g. when you
can rank the selections in order but the data is not
numerical.
• The main problem with the median is that when you have
a very large data set it can take a large amount of time to
sort the data into order.
The Mode
• The mode is the average used less frequently. It is usually
used when you have nominal/categorical data. E.g. How
do you travel to school?
• The main disadvantage with the mode is that it may not
be unique and it can be very misleading when the most
common result is a large distance away from the rest of
the data.
Quartiles
• The lower quartile shows us where a quarter (25%) of the
data items are less than and three quarters (75%) are
greater than.
• The upper quartile shows us where three quarters of the
data items are less than and one quarter greater than.
Standard Deviation
• The standard deviation gives us an idea of how spread
out the data is.
• Low SD means less spread out, high SD means more
spread out.
• Technically, for a symmetrical and unimodal data set, 95%
of the data should be within two SD’s of the mean.