Data Mining: Practical Machine Learning Tools and Techniques, Second Edition

set of numbers (the “one less than” is to do with the number of degrees of

freedom in the sample, a statistical notion that we don’t want to get into here).

The probability density function for a normal distribution with mean mand

standard deviation sis given by the rather formidable expression:

But fear not! All this means is that if we are considering a yesoutcome when

temperaturehas a value, say, of 66, we just need to plug x=66,m=73, and s=

6.2 into the formula. So the value of the probability density function is

By the same token, the probability density of a yesoutcome when humidityhas

value, say, of 90 is calculated in the same way:

The probability density function for an event is very closely related to its prob-

ability. However, it is not quite the same thing. If temperature is a continuous

scale, the probability of the temperature being exactly66—or exactlyany other

value, such as 63.14159262—is zero. The real meaning of the density function

f(x) is that the probability that the quantity lies within a small region around x,

say, between x-e/2 and x+e/2, is ef(x). What we have written above is correct

f humidity( = 90 yes)=0 0221..

f temperature( = yes)= e

◊

=

( - )

66 1 ◊

262

0 0340

66 73

262

2

2

p.

. ..

fx e

x

( )=

(-)

1

2

2

22

ps

m

s.

4.2 STATISTICAL MODELING 93

Table 4.4 The numeric weather data with summary statistics.

Outlook Temperature Humidity Windy Play

yes no yes no yes no yes no yes no

sunny 2 3 83 85 86 85 false 6 2 9 5
overcast 4 0 70 80 96 90 true 3 3
rainy 3 2 68 65 80 70
64 72 65 95
69 71 70 91
75 80
75 70
72 90
81 75

sunny 2/9 3/5 mean 73 74.6 mean 79.1 86.2 false 6/9 2/5 9/14 5/14
overcast 4/9 0/5 std. dev. 6.2 7.9 std. dev. 10.2 9.7 true 3/9 3/5
rainy 3/9 2/5