Chapter 3 Descriptive Statistics, Probability, Measures of Central Tendency

Chapter 3: Descriptive Statistics, Probability, Measures of Central Tendency New Vocabulary: Central Tendency: an indicator for the center of the data Mean: the average of the set of data Median: the middle value in a set of data Mode: the most frequently occurring value in a data set Range: the difference between the maximum and minimum values Normal distribution: a probability distribution in which the mean, median, and mode are equal Measures of Central Tendency -​ Defining the central tendency of a distribution depends of the data’s level of measurement (NOIR) -​ The only measure for nominal data is mode, which can be unimodal, bimodal, or multimodal depending on the number of peaks in the frequency distribution graph -​ Data that is rank-ordered (ordinal, interval, and ratio) can have a median in which you find the middle value of a set of data points -​ The mean can only be calculated for interval and ratio level data Range and Standard Deviation -​ The range is the difference between the maximum value and the minimum value -​ The standard deviation is the average distance of the variables from the variables mean -​ When the spread is large it is heterogeneous -​ When the spread is small it is homogenous -​ You do not need to calculate the standard deviation -​ Interquartile range can be found on a box and whiskers plot, in which interquartile range is the middle 50% of the data points -​ Outliers are values in a data set that are far spread from the rest of the data Inferential Statistics -​ Inferential statistics involves associating probabilities with each variable studied -​ Probability is the chance that a particular outcome will occur -​ Probability ranges from 0-1 Frequency Distributions vs. Probability Distributions -​ Frequency distributions involves the frequency of possible outcomes or observations in which you count the amount of times each outcome occurs -​ Probability distributions graphs the probability of all possible outcomes of the variable rather than their frequency -​ The sum of all probabilities is 1, meaning that the area under the curve is always equal to 100% -​ Probability distributions help when looking for associations between variables, and these test produce a p-value, which is the probability of finding the outcome you observed if the null hypothesis is true -​ Low p-value = good -​ High p-value = bad The Normal Distribution -​ The normal distribution is a probability distribution in which the mean, median and mode are equal (It is also called a bell curve) -​ 68/95/99 rule: -​ 68% of values fall within 1 standard deviation -​ 95% of values fall within 2 standard deviations -​ 99% of values fall within 3 standard deviations -​ In normal distributions we can calculate the Z-score, which is a standardized test measure that tells you how many standard deviations the observation is from the mean -​ Value above the mean = positive Z-score -​ Value below the mean = negative Z-score Skewed Distributions -​ They have an asymmetric distribution so that one tail is longer than the other -​ When the outliers are on the right, the skew is positive -​ When the outliers are on the left, the skew is negative -​ In skewed distributions the mean, median, and mode are not equal