histogram(~ undulation.rate, data=GlidingSnakes, n=7,
xlab = "Undulation rate (Hz)",
type = "count",
breaks = seq(0.8,2.2, by=0.2)
)
# Sample mean
n <- length(GlidingSnakes$undulation.rate)
sum(GlidingSnakes$undulation.rate) / n
mean(GlidingSnakes$undulation.rate)
# Table 3.1-1
gs <- GlidingSnakes # shorter name for data frame
table <- cbind(
observation = gs$undulation.rate,
deviation = gs$undulation.rate - mean(gs$undulation.rate),
"squared deviation" = (gs$undulation.rate - mean(gs$undulation.rate))^2
)
table
# Column sums
apply(table,2,sum)
round(rbind(table, apply(table,2,sum)),7)
# Sample variance
with(gs, sum( (undulation.rate - mean(undulation.rate))^2 ) / (n - 1))
var(gs$undulation.rate)
# Standard deviation equals the square root of the variance
sd(gs$undulation.rate)
sd(gs$undulation.rate)^2 - var(gs$undulation.rate)
# CV
sd(gs$undulation.rate) / mean(gs$undulation.rate)
100 * sd(gs$undulation.rate) / mean(gs$undulation.rate)
n <- sum(Convictions$boys)
# mean number of convictions
Ybar <- with(Convictions,
sum(convictions * boys / n))
Ybar
# Sum of squares
SS <- with( Convictions,
sum( (convictions-Ybar)^2 * boys) )
SS
# Variance
SS / (n - 1)
# Standard deviation
sqrt(SS / (n - 1))
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