# Graph description: Figure 3. Distributions for the score from rolling a single die, the mean of two dice scores, the mean of four dice scores, and the mean of six dice scores

This graph has four distinct panels, each with a separate graphic.

In the first panel, the horizontal axis is labeled "Single die score" and is numbered 1, 2, 3, 4, 5, 6. The vertical axis is labeled "Proportion of rolls" and is numbered 0, 0.05, 0.1, 0.15, 0.2, 0.25.

Vertical lines rise from the hoizontal axis at each integer. They all have the same height, which is 0.167.

At the top of the graph is written "Mean = 3.5 SD = 1.71".

In the second panel, the horizontal axis is labeled "Mean of two dice scores" and is numbered 1, 2, 3, 4, 5, 6. The vertical axis is labeled "Proportion of rolls" and is numbered 0, 0.05, 0.1, 0.15, 0.2.

Vertical lines rise from the hoizontal axis as follows: mean score = 1, proportion of rolls = 0.0278, mean score = 1.5, proportion of rolls = 0.0556, mean score = 2, proportion of rolls = 0.0833, mean score = 2.5, proportion of rolls = 0.1111, mean score = 3, proportion of rolls = 0.1389, mean score = 3.5, proportion of rolls = 0.1667, mean score = 4, proportion of rolls = 0.1389, mean score = 4.5, proportion of rolls = 0.1111, mean score = 5, proportion of rolls = 0.0833, mean score = 5.5, proportion of rolls = 0.0556, mean score = 6, proportion of rolls = 0.0278.

The tops of the vertical lines form a triangle. The apex is at mean dice score = 3.5.

At the top of the graph is written "Mean = 3.5 SD = 1.21".

In the third panel, the horizontal axis is labeled "Mean of four dice scores" and is numbered 1, 2, 3, 4, 5, 6. The vertical axis is labeled "Proportion of rolls" and is numbered 0, 0.05, 0.1, 0.15.

Vertical lines rise from the hoizontal axis as follows: mean score = 1, proportion of rolls = 0.0008, mean score = 1.25, proportion of rolls = 0.0031, mean score = 1.5, proportion of rolls = 0.0077, mean score = 1.75, proportion of rolls = 0.0154, mean score = 2, proportion of rolls = 0.0270, mean score = 2.25, proportion of rolls = 0.0432, mean score = 2.5, proportion of rolls = 0.0617, mean score = 2.75, proportion of rolls = 0.0802, mean score = 3, proportion of rolls = 0.0965, mean score = 3.25, proportion of rolls = 0.1080, mean score = 3.5, proportion of rolls = 0.1127, mean score = 3.75, proportion of rolls = 0.1080, mean score = 4, proportion of rolls = 0.0965, mean score = 4.25, proportion of rolls = 0.0802, mean score = 4.5, proportion of rolls = 0.0617, mean score = 4.75, proportion of rolls = 0.0432, mean score = 5, proportion of rolls = 0.0270, mean score = 5.25, proportion of rolls = 0.0154, mean score = 5.5, proportion of rolls = 0.0077, mean score = 5.75, proportion of rolls = 0.0031, mean score = 6, proportion of rolls = 0.0008.

The tops of the vertical lines do not form a triangle but a curve. The shape is symmetical about mean = 3.5.

At the top of the graph is written "Mean = 3.5 SD = 0.85".

In the fourth panel, the horizontal axis is labeled "Mean of six dice scores" and is numbered 1, 2, 3, 4, 5, 6. The vertical axis is labeled "Proportion of rolls" and is numbered 0, 0.05, 0.1.

Vertical lines rise from the hoizontal axis as in the previous panels. The lines are at intervals of one sixth. The vertical lines appear above the axis only between mean score = 1.5 and 5.5. As in the first three panels, the shape is symmetical about mean dice score = 3.5. The tops of the vertical lines form a curve similar to that in the third panel.

At the top of the graph is written "Mean = 3.5 SD = 0.70".

Back to Estimation.

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