Measures of Spread
Ľubica and Ján Krauskovi, Dominik Heger
Masaryk University hegerdfSchemi. muni, cz
STDT 04 Measures of Spread
skovi, Dominik Heger (K
Measures of Spread
How can we quantify your distance from the median and/or mean?
iskovi, Dominik Heger (K Measures of Spread STDT 04 Measures of Spread 2/6
Measures of Spread
How can we quantify your distance from the median and/or mean? How far from average am I?
skovi, Dominik Heger (K
Measures of Spread
How can we quantify your distance from the median and/or mean? How far from average am I? How much am I deviating?
Measures of Spread
How can we quantify your distance from the median and/or mean? How far from average am I? How much am I deviating?
The amount your score is off (from average) is the deviation.
iskovi, Dominik Heger (K Measures of Spread STDT 04 Measures of Spread 2/6
Range and interquartile range
iskovi, Dominik Heger (K Measures of Spread STDT 04 Measures of Spread 3/6
Range and interquartile range
How far from median?
iskovi, Dominik Heger (K Measures of Spread STDT 04 Measures of Spread 3/6
Range and interquartile range
How far from median?
Maternal ages
Range and interquartile range
How far from median?
Maternal ages
skovi, Dominik Heger (K
Box plot
Deviation from average
What is the typical (standard) deviation from average?
skovi, Dominik Heger (K
1 -o^o
Deviation from average
What is the typical (standard) deviation from average?
skovi, Dominik Heger (K
1 -o^o
Deviation from average
What is the typical (standard) deviation from average?
skovi, Dominik Heger (K
1 -o^o
Deviation from average
What is the typical (standard) deviation from average?
SD = standard deviation = směrodatná odchylka
= (square) root mean square of deviations from average
= (druhá) odmocnina průměru čtverců odchylek od průměru
variance = rozptyl
= mean square of deviations from average = průměr čtverců odchylek od průměru
iskovi, Dominik Heger (K
Measures of Spread
STDT 04 Measures of Spread
4/6
Properties of SD
Why SD is so commonly used measure of spread?
SD for given distribution meausres typical distance from average.
O It is non negative
Q It has the same units as average and the list.
Q It measures the average distance from the data to their mean (rms of the deviations of the data from their mean)
Q Chebychev inequality Pafnuty Lvovich Chebychev (1821 - 1894)
In any list, the proportion of entries that are k or more SDs away from the average is a       it 1/k2.
Pro jakoukoli číselnou řadu platí: podíl členů, které jsou od průměru vzdáleny alespoň /c-krát SD je n      e l/k2.
iskovi, Dominik Heger (K Measures of Spread STDT 04 Measures of Spread 5/6
Infromation sources
h tt ps: / / co u rses. edx. org/ co u rses/ Be r ke I eyX / St a t_2. lx/
http://www.stat.berkeley.edu/ stark/SticiGui/Text/location.htm
skovi, Dominik Heger (K