How can I, in R calculate the overall variance and the variance for each group from a dataset that looks like this (for example):
Group Count Value
A 3
Here's a quick wrapper with base R. First step is to grow your data set by Count, and then calculate variance by group
df1 <- df[rep(seq_len(nrow(df)), df$Count), ]
with(df1, tapply(Value, Group, var))
# A B
# 2.7 4.0
Or similarly
aggregate(Value ~ Group, df1, function(x) c(Var = var(x), Count = length(x)))
# Group Value.Var Value.Count
# 1 A 2.7 5.0
# 2 B 4.0 4.0