A data set has a sample mean of 55 and a median of 56.5 with a standard deviation of 5. Using the Pearson Coefficient, determine if the data set is normal.

The Pearson Coefficient, also known as the skewness coefficient, can be used to determine if a data set follows a normal distribution. A normal distribution has a skewness of 0.

However, in the question provided, there is not enough information to calculate the Pearson Coefficient. We need to know the mode of the data set to calculate skewness.

The formula for Pearson's Coefficient of skewness is:

Skewness = 3 * (Mean - Median) / Standard Deviation

If the skewness is less than -1 or greater than 1, the distribution is highly skewed. If it is between -1 and -0.5 or between 0.5 and 1, it is moderately skewed. If the skewness is between -0.5 and 0.5, the distribution is approximately symmetric.

So, without the mode, we cannot determine if the data set is normal.