← SASnRCumulative Sum, Mean, and Product

Introduction

Running totals show up everywhere — cumulative exposure, cumulative score, running product for compounding, rolling average for trends.
A cumulative function takes a vector and returns a vector of the same length where each element is the accumulated result up to that point.
SAS reaches for RETAIN inside a DATA step, together with sum statements (cum_sum + score;) for addition and explicit multiplication for products.
R has built-ins: cumsum() for running sum, cumprod() for running product, and derived forms for running average.
Running average is a quotient of the running sum and the running row count — both SAS and R build it the same way.
This lesson computes running sum, product, and average on a five-row score vector so every step is easy to verify.

Cumulative Sum, Mean, and Product

SAS (Base SAS)+

data scores;
    input id score;
    datalines;
1 10
2 15
3 20
4 25
5 30
;
run;

data cumulative;
    set scores;
    retain cum_sum cum_prod cum_avg count;

    if _n_ = 1 then do;
        cum_sum = score;
        cum_prod = score;
        count = 1;
        cum_avg = score;
    end;
    else do;
        cum_sum + score;
        cum_prod = cum_prod * score;
        count + 1;
        cum_avg = cum_sum / count;
    end;
run;

In SAS, cumulative operations live inside a DATA step with a RETAIN statement holding the running totals.
We initialise all accumulators on the first row: if _n_ = 1 then do; cum_sum = score; cum_prod = score; count = 1; cum_avg = score; end;.
On every subsequent row we update each accumulator: cum_sum + score; adds to the running sum using the sum-statement shortcut.
cum_prod = cum_prod * score; multiplies the running product by the new value — no shortcut operator exists for multiplication.
count + 1; counts how many rows have been processed; cum_avg = cum_sum / count; derives the running average.
The sum-statement form (var + expr;) retains the variable and treats missing values as zero — a quiet convenience built into the SAS language.
We run and verify the CUMULATIVE dataset: cum_sum grows monotonically, cum_prod multiplies through, and cum_avg is the running mean.

R (tidyverse)+

library(tidyverse)

scores <- tribble(
  ~id, ~score,
  1, 10,
  2, 15,
  3, 20,
  4, 25,
  5, 30
)

cumulative <- scores %>%
  mutate(
    cum_sum = cumsum(score),
    cum_prod = cumprod(score),
    cum_avg = cum_sum / row_number()
  )

In tidyverse, the three cumulative forms fit in a single mutate() call, using built-in functions cumsum, cumprod, and row_number.
cumsum(score) returns a vector of running totals — position i is the sum of the first i values.
cumprod(score) returns a vector of running products — position i is the product of the first i values.
For the running average, we divide the cumulative sum by the running row count: cum_avg = cum_sum / row_number().
row_number() inside mutate() gives 1, 2, 3, ... — the running count we need as the denominator.
If the data is grouped, wrap these in group_by() so the cumulatives reset at each group boundary.
We run and compare CUMULATIVE against the SAS output — the three derived columns should match row for row.

Happy learning!

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Introduction

Cumulative Sum, Mean, and Product