Assessment, Statistics, and Research

  The bell curve is also known as the normal curve or normal distribution . The bell curve has mathematical  properties that allow researchers to draw conclusions about where scores (or data) are located relative to other scores (or data). Click hyperlinks for more details. The three measures of central tendency (mode, median, mean ) are at the same middle point in a normal curve. The numbers representing the middle of the bell curve divide the distribution in half. On the x -axis in the normal distribution, the mean is at zero and there are standard deviation units above and below the mean.  The height of the curve indicates the percentage of scores in that are a. You can see that a large percentage of the scores are between 1 and -1 standard deviations. About 68% of scores fall between +1 and -1 standard deviations from the mean.  Look at the illustration below to see that there are about 34% of the scores in falling one standard deviation above the mean and an...

Who would think that a simple statistic like a mean or a median would make a difference? In large samples involving thousands of people, and when data are normally distributed (close to the shape of a bell curve), the mean and median will be nearly the same. In fact, in a theoretical distribution called the normal curve , the mean , median , and   mode are in the middle. But, many samples are not normal distributions . Instead, the often contain extreme scores called outliers or a lot of scores bunched up at high or low levels ( skewed ). Sadly, even people that understand statistics, continue to report the mean as if they are not thinking about their samples. Suppose you work for a company where the top person earns $300,000 but most folks earn $30,000 to $60,000. Well that $300,000 is gonna skew results and the mean will look much higher than the median. I ran some fictitious data on a sample of 10 people. Nine earn between $30 and $60K and one earns $300K. The Mean ...