Rolling the Dice An experiment was conducted in which two fair dice were thrown 100 times. The sum of the pips showing on the dice was then recorded. The following frequency histogram gives the results.
f. Describe the shape of the distribution.

Verified step by step guidance

1. Observe the histogram which shows the frequency of sums obtained from rolling two dice 100 times. The x-axis represents the possible sums (from 2 to 12), and the y-axis represents the frequency of each sum.
2. Notice that the frequencies increase from the lower sums, reach a peak around the middle sums (specifically at 7 or 8), and then decrease symmetrically towards the higher sums.
3. This pattern suggests that the distribution is roughly symmetric, with the highest frequency near the center of the range of possible sums.
4. The shape resembles a bell-shaped curve, which is typical for the sum of two dice because there are more combinations that result in middle sums (like 7) than extreme sums (like 2 or 12).
5. Therefore, describe the shape of the distribution as approximately symmetric and unimodal, with a peak around the sum of 7 or 8.

Key Concepts

Shape of a Distribution

The shape of a distribution describes the overall pattern of data values when plotted, such as symmetric, skewed, uniform, or bimodal. It helps in understanding the nature of the data and identifying any patterns or anomalies. For example, a symmetric distribution has roughly equal frequencies on both sides of the center.

Frequency Histogram

A frequency histogram is a graphical representation showing the number of observations (frequency) for different intervals or categories. It helps visualize the distribution of data, making it easier to identify the shape, center, and spread. In this case, it shows how often each sum of two dice occurred.

Probability Distribution of Dice Sums

When rolling two fair dice, the sums range from 2 to 12, with some sums more likely than others due to the number of combinations producing them. For example, 7 is the most common sum because it can be made in six ways, leading to a peak in the distribution. Understanding this helps explain the histogram's shape.