Name: Section: Mean and Standard Deviation Univariate Statistics for Quantitative Variables Application: To obtain a summary of the distribution of scores (center and spread) for a quantitative variable. The data: The researcher is interested in describing the data about the number of sh displayed in the Pet stores. Specically, the researcher wants to tell what is the typical number of sh displayed. The data from the 12 stores are displayed below. 32 41 31 38 21 13 17 22 24 11 17 20 Computing the Mean Step 1 Anange the data into a column The variable is referred to as X, to simplify the presentation and use of the formulas below. shnum X 32 41 31 38 21 13 17 22 24 11 17 20 Step 2 Compute the sum of the scores EX = Step 3 Determine the sample size N: 20 Step 2 Compute the sum of the scores 2X = Step 3 Determine the sample size N = Step 4 Compute the mean (always compute and report 2 decimal places) 2X 3; = = = N Computing the Standard Deviation Step 5 Compute the square of each score and place it in an adjacent column. shnum X X2 32 41 31 38 21 Espinoza, PSYC 202 Research Methods Page of 2 ZOOM + Espinoza, PSYC 202 Research Methods Step 5 Compute the square of each score and place it in an adjacent column. fishnum X X2 32 41 31 38 21 13 17 22 24 11 17 20 Step 6 Compute the sum of the squared scores EX2 = Step 7 Compute the sum of squares (EX)2 SS = EX2 . ....- - ----- = N Step 8 Compute the variance SS $2 = N-1 Step 9 Compute the standard deviation s = Std = SD = V s2 =VStep 6 Compute the sum of the squared scores 2X2 = Step 7 Compute the sum of squares 03X)2 SS = 2X2 _ _____ = _ ______ = _ _____ = _ = N Step 8 Compute the variance Step 9 Compute the standard deviation szsm:sn:4?:4 : Computing the Standard Error of the Mean The standard error of the mean (SEM) is closely related to the standard deviation. Specically, the standard deviation tells how much scores from a sample will vary from the mean of that sample. The SEM tells how much the means of several samples taken 'om the same population will vary from each other. Step 10 Compute SEM s SEM = - = W V 20 Points Possible