diff --git a/CHANGELOG.md b/CHANGELOG.md
index 43fbf11a0..1cd8b507e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -19,9 +19,12 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - `RPCholesky.reduce` in `coreax.solvers.coresubset` now computes the iteration step
   correctly. (https://github.com/gchq/coreax/pull/825)
 - `RPCholesky.reduce` in `coreax.solvers.coresubset` now does not produce duplicate
-  points in the coreset. (https://github.com/gchq/coreax/pull/836)
+  points in the coreset.(https://github.com/gchq/coreax/pull/836)
+- Fixed the example `examples.david_map_reduce_weighted` to prevent errors when
+  downsampling is enabled, and to make it run faster.(https://github.com/gchq/coreax/pull/821)
 - Build includes sub-packages. (https://github.com/gchq/coreax/pull/845)
 
+
 ### Changed
 
 -
diff --git a/examples/david_map_reduce_weighted.py b/examples/david_map_reduce_weighted.py
index 44cdbe151..f6893adba 100644
--- a/examples/david_map_reduce_weighted.py
+++ b/examples/david_map_reduce_weighted.py
@@ -44,7 +44,6 @@
 import jax.numpy as jnp
 import matplotlib.pyplot as plt
 import numpy as np
-from flax import linen
 from jax import random
 
 from coreax import (
@@ -104,32 +103,51 @@ def main(
     if out_path is not None and not out_path.is_absolute():
         out_path = Path(__file__).parent.joinpath(out_path)
 
+    def downsample_opencv(image_path: str, downsampling_factor: int) -> np.ndarray:
+        """
+        Downsample an image using `func: cv2.resize` and convert it to grayscale.
+
+        :param image_path: Path to the input image file.
+        :param downsampling_factor: Factor by which to downsample the image.
+        :return: Grayscale image after downsampling.
+        """
+        img = cv2.imread(image_path)
+
+        # Calculate new dimensions based on downsampling factor
+        scale_factor = 1 / downsampling_factor
+        width = int(img.shape[1] * scale_factor)
+        height = int(img.shape[0] * scale_factor)
+        dim = (width, height)
+
+        # Resize using INTER_AREA for better downsampling
+        resized = cv2.resize(img, dim, interpolation=cv2.INTER_AREA)
+
+        # Convert to grayscale after resizing
+        grayscale_resized = cv2.cvtColor(resized, cv2.COLOR_BGR2GRAY)
+
+        return grayscale_resized
+
     # Path to original image
-    original_data = cv2.imread(str(in_path))
-    image_data = np.asarray(cv2.cvtColor(original_data, cv2.COLOR_BGR2GRAY))
-    # Pool/downsample the image
-    window_shape = (downsampling_factor, downsampling_factor)
-    pooled_image_data = linen.avg_pool(
-        image_data[..., None], window_shape, strides=window_shape
-    )[..., 0]
-    block_size = 1_000 // downsampling_factor
-
-    print(f"Image dimensions: {pooled_image_data.shape}")
-    pre_coreset_data = np.column_stack(np.nonzero(pooled_image_data < MAX_8BIT))
-    pixel_values = pooled_image_data[pooled_image_data < MAX_8BIT]
+    original_data = downsample_opencv(str(in_path), downsampling_factor)
+
+    block_size = 1_000 // (downsampling_factor**2)
+
+    print(f"Image dimensions: {original_data.shape}")
+    pre_coreset_data = np.column_stack(np.nonzero(original_data < MAX_8BIT))
+    pixel_values = original_data[original_data < MAX_8BIT]
     pre_coreset_data = np.column_stack((pre_coreset_data, pixel_values)).astype(
         np.float32
     )
     num_data_points = pre_coreset_data.shape[0]
 
     # Request coreset points
-    coreset_size = 8_000 // downsampling_factor
+    coreset_size = 8_000 // (downsampling_factor**2)
 
     # Setup the original data object
     data = Data(pre_coreset_data)
 
     # Set the length_scale parameter of the kernel from at most 1000 samples
-    num_samples_length_scale = min(num_data_points, 1000 // downsampling_factor)
+    num_samples_length_scale = min(num_data_points, 1000 // (downsampling_factor**2))
     random_seed = 1_989
     generator = np.random.default_rng(random_seed)
     idx = generator.choice(num_data_points, num_samples_length_scale, replace=False)
@@ -159,10 +177,10 @@ def main(
     herding_solver = KernelHerding(
         coreset_size,
         kernel=herding_kernel,
-        block_size=1_000 // downsampling_factor,
+        block_size=block_size,
     )
     mapped_herding_solver = MapReduce(
-        herding_solver, leaf_size=10_000 // downsampling_factor
+        herding_solver, leaf_size=16_000 // (downsampling_factor**2)
     )
     herding_coreset, _ = eqx.filter_jit(mapped_herding_solver.reduce)(data)
     herding_weights = weights_optimiser.solve(data, herding_coreset.coreset)
@@ -192,11 +210,44 @@ def main(
     print(f"Random sampling coreset MMD: {random_mmd}")
     print(f"Herding coreset MMD: {herding_mmd}")
 
+    def transform_marker_size(
+        weights: np.ndarray,
+        scale_factor: int = 15,
+        min_size: int = 4 * downsampling_factor,
+    ) -> np.ndarray:
+        """
+        Transform coreset weights to marker sizes for plotting.
+
+        :param weights: Array of coreset weights to be transformed.
+        :param scale_factor: Ratio of the largest and the smallest marker sizes.
+        :param min_size: Smallest marker size.
+        :return: Array of transformed marker sizes for plotting.
+        """
+        # Define threshold percentiles
+        lower_percentile, upper_percentile = 1, 99
+
+        # Clip weights to reduce the effect of outliers
+        clipped_weights = np.clip(
+            weights,
+            np.percentile(weights, lower_percentile),
+            np.percentile(weights, upper_percentile),
+        )
+
+        # Normalize weights to a [0, 1] range
+        normalized_weights = (clipped_weights - clipped_weights.min()) / (
+            clipped_weights.max() - clipped_weights.min()
+        )
+
+        # Apply exponential scaling to get the desired spread
+        transformed_sizes = min_size + (scale_factor**normalized_weights - 1) * min_size
+
+        return transformed_sizes
+
     print("Plotting")
     # Plot the pre-coreset image
     plt.figure(figsize=(10, 5))
     plt.subplot(1, 3, 1)
-    plt.imshow(pooled_image_data, cmap="gray")
+    plt.imshow(original_data, cmap="gray")
     plt.title("Pre-Coreset")
     plt.axis("off")
 
@@ -208,7 +259,7 @@ def main(
         -herding_coreset.coreset.data[:, 0],
         c=herding_coreset.coreset.data[:, 2],
         cmap="gray",
-        s=np.exp(2.0 * coreset_size * herding_weights).reshape(1, -1),
+        s=(transform_marker_size(herding_weights)).reshape(1, -1),
         marker="h",
         alpha=0.8,
     )
@@ -222,7 +273,7 @@ def main(
         random_coreset.coreset.data[:, 1],
         -random_coreset.coreset.data[:, 0],
         c=random_coreset.coreset.data[:, 2],
-        s=1.0,
+        s=25 * downsampling_factor,
         cmap="gray",
         marker="h",
         alpha=0.8,
@@ -248,4 +299,4 @@ def main(
 
 
 if __name__ == "__main__":
-    main()
+    main(out_path=Path("data/david_coreset_2.png"))