The formula for calculating the z-score of any particular data set is z = (x - μ) / σ where μ is the mean of a population and σ is the standard deviation of a population. The absolute value of z represents the z-score of the population, the distance between the raw score and population mean in units of standard deviation. TABLE B. 1 THE UNIT NORMAL TABLE* *Column A lists a-score values. A vertical line drawn through a normal distribution at a z-score location divides the distri- bution into two sections. Column B identifies the proportion in the larger section, called the body. Column C identifies the proportion in the smaller section, called the tail. Basic Statistics Formulas Population Measures Mean = 1 n X x i (1) Variance ˙2 = 1 n X (x i x)2 (2) Standard Deviation ˙= r 1 n X (x i x)2 (3) Sampling Sample mean x= 1 n X x i (4) Sample variance s2 x = 1 n 1 X (x i x)2 (5) Std. Deviation s x = r 1 n 1 X (x i x)2 (6) z-score z= x ˙ (7) Correlation r= 1 n 1 Xn i=1 (x i x) s x (y i y) s y (8) Linear Regression Line ^y= a+ bx (9) b= r s y s x;a= y bx (10) s= v u u t 1 n 2 Xn i=1 Statistics tables including the standard normal table / z table, t table, F table, Chi-square table. Probability distributions including the normal distribution, t distribution, F distribution, Chi-square distribution. AP Statistics Student Resource Packet The fol lowing formula s and tables are similar t o the ones which wil l be pro vided t o you on the A dvanc ed Plac ement Exam. Y ou wil l be al low ed t o use the fol lowing resourc es on select Quizzes and Exams a s w e proc eed through the course. K eep this pack et in an acc essible plac e !such a s
Z Score Table- chart value corresponds to area below z score. z 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 –3.4 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 .50000 .50399 .50798 .51197 .51595
TABLE B. 1 THE UNIT NORMAL TABLE* *Column A lists a-score values. A vertical line drawn through a normal distribution at a z-score location divides the distri- bution into two sections. Column B identifies the proportion in the larger section, called the body. Column C identifies the proportion in the smaller section, called the tail. Basic Statistics Formulas Population Measures Mean = 1 n X x i (1) Variance ˙2 = 1 n X (x i x)2 (2) Standard Deviation ˙= r 1 n X (x i x)2 (3) Sampling Sample mean x= 1 n X x i (4) Sample variance s2 x = 1 n 1 X (x i x)2 (5) Std. Deviation s x = r 1 n 1 X (x i x)2 (6) z-score z= x ˙ (7) Correlation r= 1 n 1 Xn i=1 (x i x) s x (y i y) s y (8) Linear Regression Line ^y= a+ bx (9) b= r s y s x;a= y bx (10) s= v u u t 1 n 2 Xn i=1 Statistics tables including the standard normal table / z table, t table, F table, Chi-square table. Probability distributions including the normal distribution, t distribution, F distribution, Chi-square distribution. AP Statistics Student Resource Packet The fol lowing formula s and tables are similar t o the ones which wil l be pro vided t o you on the A dvanc ed Plac ement Exam. Y ou wil l be al low ed t o use the fol lowing resourc es on select Quizzes and Exams a s w e proc eed through the course. K eep this pack et in an acc essible plac e !such a s
It tells us the area under the standard normal curve for any value between the mean (zero) and any z-score. Why Are There at least Two z-tables? Simply, it's to Z tables use at least three different conventions: Cumulative from mean: gives a probability that a statistic is between 0 (mean) and Z. Example: Prob(0 ≤ Z 02,, 3.99. Pr (Z>z) = ∫ ∞ z. 1. √2π e.
It tells us the area under the standard normal curve for any value between the mean (zero) and any z-score. Why Are There at least Two z-tables? Simply, it's to Z tables use at least three different conventions: Cumulative from mean: gives a probability that a statistic is between 0 (mean) and Z. Example: Prob(0 ≤ Z 02,, 3.99. Pr (Z>z) = ∫ ∞ z. 1. √2π e. The z-score is positive if the value lies above the mean, and negative if it lies below the mean. Learn how to use a z-score table Download this article as a PDF What a p-value Tells You About Statistical Significance Confidence Intervals To use the Z-table to find probabilities for a statistical sample with a standard normal (Z-) distribution, do the following: Go to the row that represents the ones digit