measures of dispersion: range and standard deviation

the range

-the difference between the highest and the lowest in a data set

and then ADD 1

the range: strengths

-provides you with direct information on the dispersion of the data that is easy to calculate

the range: limitations

-affected by extreme values

-doesnt take into account all of the numbers in the data set

-doesnt consider the distribution of the data within the range

standard deviation

(not required to calculate in the exam)

-shows how much variation from the mean/average exists

-a low standard deviation indicates that the data points tend to be very close to the mean

-a high standard deviation indicates that the data points are spread out ogver a large range of values

what percent of the data will be found in 1 standard deviation?

68%

what percent of the data will be found in 2 standard deviation?

95%

what percent of the data will be found in 3 standard deviation?

99.7%

standard deviation: strengths

-more precise measure which takes all the values into account so will consider the distribution within the data set

-less likely to be distorted by a single anomolous datum if data are many

standard deviation: limitations

-can therefore be affected by outliers or anomolous data if data are few