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Understanding how to calculate the mean of a dataset is an essential skill in descriptive statistics. The mean, sometimes called the average, offers a quick glance at the central tendency of a dataset.

To determine the mean, you sum up all the data points and then divide this total by the number of data points in the set. For example, if you have a list of times in seconds like 15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1, and 29.4, you would first add these values together to get the total sum, which is 166.5 seconds.

Next, since there are 8 participants, you divide the total by 8, thus:

• Mean = \( \frac{166.5}{8} = 20.8125 \) seconds

This mean value tells us the average time it took for participants to solve the puzzle.

The median is another measure of central tendency, but it tells us a different story than the mean. It pinpoints the middle value of a dataset, where half the numbers are smaller and the other half are larger.

To find the median in a sorted list with an even number of values, such as our dataset of times, you take the average of the two middle numbers. In our data:

• The 4th time is 19.7 seconds.
• The 5th time is 20.2 seconds.

Calculate the median by averaging these two numbers:

• Median = \( \frac{19.7 + 20.2}{2} = 19.95 \) seconds

This tells us that in the central position of our dataset, the time is 19.95 seconds.

Comparing the mean and the median provides insights into the shape of data distribution. This comparison helps determine whether a dataset is symmetric, skewed left, or skewed right.

In a symmetric distribution, the mean and the median are generally equal or very close to each other. However, if the mean is greater than the median, as seen with our dataset (mean = 20.8125, median = 19.95), it indicates that the distribution is skewed to the right.

A right-skewed distribution often occurs when a few high values are dragging the mean upwards. These outliers effect the overall average more than the central median, creating skewness. Understanding these dynamics helps in interpreting data accurately and applying the best statistical practices in analysis.