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Showing posts with the label normal distribution

### Kurtosis

Kurtosis is a statistical concept. The value indicates whether a distribution is similar to the normal curve or different from the normal curve. Compared to the normal curve, kurtotic distributions of data appear either peaked in the middle or flat. In a normal distribution, the value of kurtosis = 0. The peaked distribution has a positive value. It's called leptokurtic (think leap). The flatter distribution has a negative value. It's called platykurtic (think of the animal, Platypus). There are different formulas for calculating kurtosis. In Excel, the function for kurtosis can be found under Formulas, More Functions. In the drop down list, choose KURT. Please check out my website     www.suttong.com    and see my books on    AMAZON         or   GOOGLE STORE Also, consider connecting with me on     FACEBOOK     Geoff W. Sutton         TWITTER    @Geoff.W.Sutton     You can read many published articles at no charge:   Academia    Geoff W Sutton       ResearchGate

### Normal Distribution or Bell Curve

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 another 34% in one st

### Skewed Distributions

Skewed Distributions* Skewed distributions have one tail that is longer than the other tail compared to the "normal" distribution, which is perfectly symmetrical. Skew affects the location of the central values of the mean and median. Positive Skew Below is an image of positive skew, which is also called right skew. Skew is named for the "tail." If you had statistics, you may have heard a professor say, "the tail tells the tale." The tail is the extended part of the distribution close to the horizontal axis. The large "hump" area to the left represents the location of most data. In behavioural science, the high part often refers to the location of most of the scores. Thus, in positively skewed distributions, most of the participants earned low scores and few obtained high scores as you can see by the low level of the curve, or the tail, to the right. Negative Skew As you might expect, negatively skewed distributions have the long tail on the le

### Reporting Mean or Median

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 = \$6