Calculating a group mean while excluding each cases individual value

Question

I have a dataset with 70 cases (participants in a study). Is there a function that can calculate the mean of these 70 cases such that each individual case is not included in the analysis. This would look like:

"mean for case x = (value(1) + ... value(n) - value(x))/n"

Any information will help.

Answer 1

You could just do what you've suggested and remove each case from the total:

x <- c(1:10)
(sum(x) - x) / (length(x) - 1)

#[1] 6.000000 5.888889 5.777778 5.666667 5.555556 5.444444 5.333333 5.222222 5.111111 5.000000

mean(2:10)
#[1] 6
mean(1:9)
#[1] 5

EDIT: Updated to try to address followup question in comments:

set.seed(123)
df <- data.frame(group = rep(letters[1:3], each = 3), 
                 value = rnorm(9), stringsAsFactors = F)
df

#group       value
#1     a -0.56047565
#2     a -0.23017749
#3     a  1.55870831
#4     b  0.07050839
#5     b  0.12928774
#6     b  1.71506499
#7     c  0.46091621
#8     c -1.26506123
#9     c -0.68685285

df$loo_mean <- unlist(tapply(df$value, df$group, 
                      function(x) (sum(x) - x) / (length(x) - 1)))
df

  #group       value    loo_mean
#1     a -0.56047565  0.66426541
#2     a -0.23017749  0.49911633
#3     a  1.55870831 -0.39532657
#4     b  0.07050839  0.92217636
#5     b  0.12928774  0.89278669
#6     b  1.71506499  0.09989806
#7     c  0.46091621 -0.97595704
#8     c -1.26506123 -0.11296832
#9     c -0.68685285 -0.40207251

mean(df$value[2:3])
#[1] 0.6642654
mean(df$value[c(7,9)])
#[1] -0.1129683

Answer 2

Here's a vectorised approach, to avoid averaging each subset one at a time:

x <- runif(70)
sapply(seq_along(x), function(i) mean(x[-i]))