The+Standard+Deviation+as+a+Ruler+and+the+Normal+Model

Standard deviation can be used as a "ruler" in order to compare values with different scales, units or populations.

Calculator Tips!
 * Z-Score Formula: ( data value ) - (the mean) / standard deviation**

Finding the specified percentile: normalcdf(z-score from the left, z-score from the right) Finding percentage of data that is higher than a given value: normalcdf (z-score, 10^10) Finding percentage of data that is lower than a given value: normalcdf (-10^10, z-score) Finding z-score: invnorm (percentage in decimal form) = z-score

RESCALING DATA - when multiplying or dividing each data by a constant, multiply or divide the mean, median, range, IQR, and standard deviation by the same constant. ||
 * ~ **Vocabulary Word** ||~ **Definition** ||
 * Changing the Center || Adding a constant to each value adds the same constant to the mean, the median, and the quartiles but does not change the standard deviation or IQR ||
 * Changing the Scale || Multiplying each data value by a constant mutliplies both the measueres of position (mean, median, and quartiles) and measures of spread (standarad deviation and IQR) ||
 * Standardizing || when standardizing data, the mean is shifted to 0 (changing the center) and the standard deviation = 1 (changing the spread). However, the shape doesn't change. ||
 * Standardized Value || Values that have no unit and are measured in standard deviations away from the mean. ||
 * Normal Model || A bell shaped curve that follows an appropriate model if unimodal with a symmetric shape ||
 * Parameter || A quantity whose value is selected for the particular circumstances and in relation to which other variable quantities may be expressed. ||
 * Statistic || A fact or piece of data from a study of a large quantity of numerical data ||
 * z-score || calculating the z-score is equivalent to determining standardized values. It also enables comparison between different scales. The bigger the z-score, the more unusual that data is. z= (y - ybar)/(SD) ||
 * Standard Normal Model || when parameters (mean, standard deviation) are (0,1), respectively. ||
 * 68-95-99.7 Rule || (aka Empirical Rule) states that 68% of all data falls within ONE standard deviation, 95% of all all data falls within TWO standard deviations, and 99.7% falls within THREE standard deviations. ||
 * Normal Percentile || The table of Normal percentiles finds the percentage of individuals in a standard normal distribution falling BELOW a specific z-score. All data must be converted into z-scores in order to use the table. ||
 * Normal Probability Plot || shows deviations from normality (better than histograms) ||
 * Changing Center and Spread || SHIFTING DATA- when adding or subtracting a constant to or from each data value, add or subtract the same constant to the mean, median, quartiles, maximum, and minimum. the spread does not change.