05AB1E , 13 bytes
ÅAIÅ»+;}θ‚ÂÆa
Outputs as a triplet [mean, progressive-mean, trend].
Try it online or verify all test cases.
Explanation:
ÅA # Calculate the arithmetic mean of the (implicit) input-list
I # Push the input-list again
Å» # Left-reduce it by:
+ # Add the two values together
; # And halve it
}θ # After the reduction, leave only the last value
‚ # Pair it with the earlier calculated arithmetic mean
 # Bifurcate this pair; short for Duplicate & Reverse copy
Æ # Reduce it by subtraction
a # And append this trend to the pair
# (after which the result is output implicitly)
ÅAIÅ»+;}θ‚ÂÆa
Outputs as a triplet [mean, progressive-mean, trend].
Try it online or verify all test cases.
Explanation:
ÅA # Calculate the arithmetic mean of the (implicit) input-list
I # Push the input-list again
Å» # Left-reduce it by:
+ # Add the two values together
; # And halve it
}θ # After the reduction, leave only the last value
‚ # Pair it with the earlier calculated arithmetic mean
 # Bifurcate this pair; short for Duplicate & Reverse copy
Æ # Reduce it by subtraction
a # And append this trend to the pair
# (after which the result is output implicitly)
05AB1E , 13 bytes
ÅAIÅ»+;}θ‚ÂÆa
Outputs as a triplet [mean, progressive-mean, trend].
Try it online or verify all test cases.
Explanation:
ÅA # Calculate the arithmetic mean of the (implicit) input-list
I # Push the input-list again
Å» # Left-reduce it by:
+ # Add the two values together
; # And halve it
}θ # After the reduction, leave only the last value
‚ # Pair it with the earlier calculated arithmetic mean
 # Bifurcate this pair; short for Duplicate & Reverse copy
Æ # Reduce it by subtraction
a # And append this trend to the pair
# (after which the result is output implicitly)
ÅAIÅ»+;}θ‚ÂÆa
Outputs as a triplet [mean, progressive-mean, trend].
Try it online or verify all test cases.
Explanation:
ÅA # Calculate the arithmetic mean of the (implicit) input-list
I # Push the input-list again
Å» # Left-reduce it by:
+ # Add the two values together
; # And halve it
}θ # After the reduction, leave only the last value
‚ # Pair it with the earlier calculated arithmetic mean
 # Bifurcate this pair; short for Duplicate & Reverse copy
Æ # Reduce it by subtraction
a # And append this trend to the pair
# (after which the result is output implicitly)