Descriptive Statistics Measures of Correlational Strength: Perfect positive correlation: R=1 Perfect negative correlation: R=-1 Statistical significance – results of a study are not due to chance For a correlation to be statistically significant, R must be greater than .3 or less than -.3

Descriptive Statistics Central Tendency Median, Mean, & Mode The mean is the arithmetic average of a set of given numbers. The median is the middle score in a set of given numbers. The mode is the most frequently occurring score in a set of given numbers.

Best Measure of Central Tendency? $25,000- Ryan $25,000- Creed $25,000-Daryl $25,000- Kevin $25,000- Meredith $25,000-Oscar $40,000- Phyllis $50,000- Stanley $75,000- Andy $100,000- Angela $150,000- Dwight $200,000- Jim $300,000- Michael Mean=82K Median=40K Mode=25K

Descriptive Statistics Variability Standard deviation – measures variability in a data set; how much scores vary from each other and from the mean “How far from normal?” How far apart are a set of scores?

Normal Distribution In a given set of data, human characteristics are dispersed across the population in a general pattern: Where are the mean, median & mode in the normal distribution? Positive skew = home prices in neighborhood. Very pricey house (positively skewed) For example, if you are told that the average starting salary for someone working at Company Statistix is $70,000, you may think, “Wow! That’s great.” But if the standard deviation for starting salaries at Company Statistix is $20,000, that’s a lot of variation in terms of how much money you can make, so the average starting salary of $70,000 isn’t as informative in the end, is it? On the other hand, if the standard deviation was only $5,000, you would have a much better idea of what to expect for a starting salary at that company. Which is more appealing? That’s a decision each person has to make; however, it’ll be a much more informed decision once you realize standard deviation matters. Cases w/in interval 0.1% 2.1% 13.6% 34.1% 34.1% 13.6% 2.1% 0.1% St. Dev. from mean -3 -2 -1 0 1 2 3 Percentile 0.01th 2nd 16th 50th 84th 98th 99.9th

Normal Distribution What is a positively or negatively skewed distribution? What is the relationship between the mean and median/mode in a positively/negatively skewed curve? Draw! Positive skew = home prices in neighborhood. Very pricey house (positively skewed) A positively skewed distribution is asymmetrical and points in the positive direction. If a test was very difficult and almost everyone in the class did very poorly on it, the resulting distribution would most likely be positively skewed. In the case of a positively skewed distribution, the mode is smaller than the median, which is smaller than the mean. This relationship exists because the mode is the point on the x-axis corresponding to the highest point, that is the score with greatest value, or frequency. The median is the point on the x-axis that cuts the distribution in half, such that 50% of the area falls on each side. The mean is the balance point of the distribution. Because points further away from the balance point change the center of balance, the mean is pulled in the direction the distribution is skewed. For example, if the distribution is positively skewed, the mean would be pulled in the direction of the skewness, or be pulled toward larger numbers. One way to remember the order of the mean, median, and mode in a skewed distribution is to remember that the mean is pulled in the direction of the extreme scores. In a positively skewed distribution, the extreme scores are larger, thus the mean is larger than the median. Cases w/in interval 0.1% 2.1% 13.6% 34.1% 34.1% 13.6% 2.1% 0.1% St. Dev. from mean -3 -2 -1 0 1 2 3 Percentile 0.01th 2nd 16th 50th 84th 98th 99.9th

AP-type Question The typical IQ test has a mean of 100 and a standard deviation of 15. If you scored 115, what percentage of others who have taken the test scored lower than you?

Normal Distribution In a given set of data, human characteristics are dispersed across the population in a general pattern: Positive skew = home prices in neighborhood. Very pricey house (positively skewed) Cases w/in interval 0.1% 2.1% 13.6% 34.1% 34.1% 13.6% 2.1% 0.1% St. Dev. from mean -3 -2 -1 0 1 2 3 Percentile 0.01th 2nd 16th 50th 84th 98th 99.9th