diff --git a/r/R/dplyr-functions.R b/r/R/dplyr-functions.R
index efba9f287f9..843b71244ba 100644
--- a/r/R/dplyr-functions.R
+++ b/r/R/dplyr-functions.R
@@ -808,3 +808,27 @@ agg_funcs$all <- function(x, na.rm = FALSE) {
     options = list(na.rm = na.rm, na.min_count = 0L)
   )
 }
+
+agg_funcs$mean <- function(x, na.rm = FALSE) {
+  list(
+    fun = "mean",
+    data = x,
+    options = list(na.rm = na.rm, na.min_count = 0L)
+  )
+}
+# na.rm not currently passed in due to ARROW-13691
+agg_funcs$sd <- function(x, na.rm = FALSE, ddof = 1) {
+  list(
+    fun = "stddev",
+    data = x,
+    options = list(ddof = ddof)
+  )
+}
+# na.rm not currently passed in due to ARROW-13691
+agg_funcs$var <- function(x, na.rm = FALSE, ddof = 1) {
+  list(
+    fun = "variance",
+    data = x,
+    options = list(ddof = ddof)
+  )
+}
diff --git a/r/src/compute.cpp b/r/src/compute.cpp
index b697ecd96a0..dec8b2adfaa 100644
--- a/r/src/compute.cpp
+++ b/r/src/compute.cpp
@@ -350,7 +350,8 @@ std::shared_ptr<arrow::compute::FunctionOptions> make_compute_options(
                                      step);
   }
 
-  if (func_name == "variance" || func_name == "stddev") {
+  if (func_name == "variance" || func_name == "stddev" || func_name == "hash_variance" ||
+      func_name == "hash_stddev") {
     using Options = arrow::compute::VarianceOptions;
     return std::make_shared<Options>(cpp11::as_cpp<int64_t>(options["ddof"]));
   }
diff --git a/r/tests/testthat/test-dplyr-aggregate.R b/r/tests/testthat/test-dplyr-aggregate.R
index 25cd0ccabfb..b19b3891dfe 100644
--- a/r/tests/testthat/test-dplyr-aggregate.R
+++ b/r/tests/testthat/test-dplyr-aggregate.R
@@ -88,10 +88,73 @@ test_that("Group by sum on dataset", {
       summarize(total = sum(int)) %>%
       arrange(some_grouping) %>%
       collect(),
+    tbl,
+  )
+})
+
+test_that("Group by mean on dataset", {
+  expect_dplyr_equal(
+    input %>%
+      group_by(some_grouping) %>%
+      summarize(mean = mean(int, na.rm = TRUE)) %>%
+      arrange(some_grouping) %>%
+      collect(),
+    tbl
+  )
+  
+  expect_dplyr_equal(
+    input %>%
+      group_by(some_grouping) %>%
+      summarize(mean = mean(int, na.rm = FALSE)) %>%
+      arrange(some_grouping) %>%
+      collect(),
     tbl
   )
 })
 
+test_that("Group by sd on dataset", {
+  expect_dplyr_equal(
+    input %>%
+      group_by(some_grouping) %>%
+      summarize(sd = sd(int, na.rm = TRUE)) %>%
+      arrange(some_grouping) %>%
+      collect(),
+    tbl
+  )
+  
+  skip("ARROW-13691 - na.rm not yet implemented for VarianceOptions")
+  expect_dplyr_equal(
+    input %>%
+      group_by(some_grouping) %>%
+      summarize(sd = sd(int, na.rm = FALSE)) %>%
+      arrange(some_grouping) %>%
+      collect(),
+    tbl
+  )
+})
+
+test_that("Group by var on dataset", {
+  expect_dplyr_equal(
+    input %>%
+      group_by(some_grouping) %>%
+      summarize(var = var(int, na.rm = TRUE)) %>%
+      arrange(some_grouping) %>%
+      collect(),
+    tbl
+  )
+  
+  skip("ARROW-13691 - na.rm not yet implemented for VarianceOptions")
+  expect_dplyr_equal(
+    input %>%
+      group_by(some_grouping) %>%
+      summarize(var = var(int, na.rm = FALSE)) %>%
+      arrange(some_grouping) %>%
+      collect(),
+    tbl
+  )
+})
+
+
 test_that("Group by any/all", {
   withr::local_options(list(arrow.debug = TRUE))