Transcript S1 Skewness and choice of data

S1 Representing
data
Skewness and choice of
data analysis
Skewness
The first distribution shown has a positive skew. This means
that it has a long tail in the positive direction.
The distribution below it has a negative skew since it has a
long tail in the negative direction.
Finally, the third distribution is symmetric and has no skew.
Distributions with positive skew are sometimes called
"skewed to the right" whereas distributions with negative
skew are called "skewed to the left."
Skewness – visuals and calculations
Calculate Q1, Q2, Q3, mode, mean and standard
deviation
Draw all 3 boxplots on one piece of graph paper
Data set 1
Data set 2
Data set 3
1, 3, 5, 5, 5, 7, 10
2, 7, 7, 8, 12, 14, 20
3, 6, 7, 9, 10, 10, 11
•For each data set find a relationship between the mode, median
and mean using =,>,< symbols
•For each data set find a relationship between Q2-Q1 and Q3-Q2
•Work out
3(mean-median)
standard deviation
Skewness – Using the Quartiles
Q2-Q1 = Q3-Q2
Q2-Q1 < Q3-Q2
Q2-Q1 > Q3-Q2
Skewness – Using mode, median, mean
Q2-Q1 = Q3-Q2
Q2-Q1 < Q3-Q2
Mode=median=mean Mode<median<mean
Q2-Q1 > Q3-Q2
Mode>median>mean
Skewness calculations
You can calculate
3(mean-median)
Standard deviation
This gives you a value to tell you how
skewed the data are.
The closer the number to zero the more
symmetrical the data
Negative value means the data has a
negative skew and vice versa
Comparing data sets
You should always compare data sets using
•a measure of location (mean, median, mode)
•a measure of spread (range, IQR, standard deviation)
•skewness
•Range gives a rough idea of spread, but is affected by
extreme values.
•Generally only used with small data groups
•IQR not affected by extreme values
•Tells you the spread of middle 50%
•Often used in conjunction with median
•Mean and standard deviation generally used when
data are fairly symmetrical
•data size is reasonably large