Intro to Statistics with R: Introduction
Intro to Statistics with R: Introduction
Measures of central tendency
Intro to Statistics with R : Introduction
Wine ratings (revisited) ●
100 wine experts
●
Rate quality (1-100) of 8 different wines
●
4 red wines and 4 white wines
●
Higher scores = higher quality
Intro to Statistics with R : Introduction
Wine ratings (red) Country
Mean = M = (ΣX) / N
Argentina
66.73
Australia
81.76
France
70.97
USA
76.38
Intro to Statistics with R : Introduction
Wine ratings (white) Country
Mean = M = (ΣX) / N
Argentina
71.20
Australia
86.81
France
85.90
USA
88.62
Intro to Statistics with R: Introduction
Let's Practice!
Intro to Statistics with R: Introduction
Three measures of central tendency (1/2)
Intro to Statistics with R : Introduction
Measures of central tendency ●
Summary statistic
●
Middle or center point of a distribution
●
Should be representative of distribution
Intro to Statistics with R : Introduction
Measures of central tendency ●
Mean
average; (ΣX) / N
●
Median
middle score in a distribution; e.g. 50th out of 100 total
●
Mode
score that occurs most frequently; peak of the histogram
Intro to Statistics with R : Introduction
Mean (average) ●
Most common measure of central tendency
●
Example: Grade point average (GPA)
●
Best when distribution is normal
Intro to Statistics with R : Introduction
Median ●
Preferred when extreme scores in distribution
●
White wine ratings
●
Household income in USA
Intro to Statistics with R: Introduction
Let's Practice!
Intro to Statistics with R: Introduction
Three measures of central tendency (2/2)
Intro to Statistics with R : Introduction
Wine ratings (white) Positive skew Negative skew
Country
Mean = M = (ΣX) / N
Median
Argentina
71.20
71.00
Australia
86.81
86.68
France
85.90
86.00
USA
88.62
88.65
Intro to Statistics with R : Introduction
Household income Positive skew
Intro to Statistics with R : Introduction
Mode ●
Peak of the histogram
●
Score that occurs most frequently
Mode is between 70 and 72
Intro to Statistics with R : Introduction
Mode ●
Can be used for nominal variables Name
Gender
Country
Sophia
Female
USA
James
Male
USA
Emma
Female
France
Nathan
Male
France
Sofia
Female
Argentina
Juan
Male
Argentina
Charlo"e
Female
Australia
Oliver
Male
Australia
Intro to Statistics with R: Introduction
Let's Practice!
Intro to Statistics with R: Introduction
Quick summary
Intro to Statistics with R : Introduction
Summary ●
Mean
average; (ΣX) / N
●
Median
middle score in a distribution; e.g. 50th out of 100 total
●
Mode
score that occurs most frequently; peak of the histogram
Intro to Statistics with R: Introduction
Congratulations!
Measures of central tendency
Intro to Statistics with R : Introduction
Wine ratings (revisited) ●
100 wine experts
●
Rate quality (1-100) of 8 different wines
●
4 red wines and 4 white wines
●
Higher scores = higher quality
Intro to Statistics with R : Introduction
Wine ratings (red) Country
Mean = M = (ΣX) / N
Argentina
66.73
Australia
81.76
France
70.97
USA
76.38
Intro to Statistics with R : Introduction
Wine ratings (white) Country
Mean = M = (ΣX) / N
Argentina
71.20
Australia
86.81
France
85.90
USA
88.62
Intro to Statistics with R: Introduction
Let's Practice!
Intro to Statistics with R: Introduction
Three measures of central tendency (1/2)
Intro to Statistics with R : Introduction
Measures of central tendency ●
Summary statistic
●
Middle or center point of a distribution
●
Should be representative of distribution
Intro to Statistics with R : Introduction
Measures of central tendency ●
Mean
average; (ΣX) / N
●
Median
middle score in a distribution; e.g. 50th out of 100 total
●
Mode
score that occurs most frequently; peak of the histogram
Intro to Statistics with R : Introduction
Mean (average) ●
Most common measure of central tendency
●
Example: Grade point average (GPA)
●
Best when distribution is normal
Intro to Statistics with R : Introduction
Median ●
Preferred when extreme scores in distribution
●
White wine ratings
●
Household income in USA
Intro to Statistics with R: Introduction
Let's Practice!
Intro to Statistics with R: Introduction
Three measures of central tendency (2/2)
Intro to Statistics with R : Introduction
Wine ratings (white) Positive skew Negative skew
Country
Mean = M = (ΣX) / N
Median
Argentina
71.20
71.00
Australia
86.81
86.68
France
85.90
86.00
USA
88.62
88.65
Intro to Statistics with R : Introduction
Household income Positive skew
Intro to Statistics with R : Introduction
Mode ●
Peak of the histogram
●
Score that occurs most frequently
Mode is between 70 and 72
Intro to Statistics with R : Introduction
Mode ●
Can be used for nominal variables Name
Gender
Country
Sophia
Female
USA
James
Male
USA
Emma
Female
France
Nathan
Male
France
Sofia
Female
Argentina
Juan
Male
Argentina
Charlo"e
Female
Australia
Oliver
Male
Australia
Intro to Statistics with R: Introduction
Let's Practice!
Intro to Statistics with R: Introduction
Quick summary
Intro to Statistics with R : Introduction
Summary ●
Mean
average; (ΣX) / N
●
Median
middle score in a distribution; e.g. 50th out of 100 total
●
Mode
score that occurs most frequently; peak of the histogram
Intro to Statistics with R: Introduction
Congratulations!
