Descriptive Statistics: Variability and Z-scores Flashcards
Variability
Degree to which scores in a distribution are spread out or clustered together (in terms of distance)
Range
-Distance between the largest and smallest score
-Highest score - lowest score = range
-Helps see whether some of the points on a scale were covered
-Limitation- determined by 2 extreme values and ignores other scores, misleadin
Interquartile range
-Q3 - Q1 = IQR
-Box-and-whisker plot
-Limitation- discards too much of the data
Relationship between the sum of squares, variance, and standard deviation
-Sum of squares = numerator in the variance
-Variance = sum of squares/number of cases, SD^2
-Standard deviation = sqr rt of variance
Sum of squares
Sum of (x-mean)^2
Variance
Average squared distance between each score and the mean
Bessel’s correction
To adjust underestimation in variance and SD, use n-1 in the denominator in sample formulas
Normal distribution
-Described by mean and SD
-Symmetrical, unimodal, and asymptotic
Skew
-Describes the symmetry of the distribution
-Positive skew- tail extends towards higher values (right)
-Negative skew- tail extends towards lower values (left)
Kurtosis
-Describes the peak of the distribution and its tailedness
-Positive kurtosis- heavier tails and high peak (leptokurtic)
-Negative kurtosis- lighter tails and flattened center (platykurtic)
Z-scores
-Raw score - mean / SD = z
-Communicates info about the score, mean, and SD in a single value and is the primary way to standardize
-Units in SD
Z-score communicates…
-Value- the number of SD from the mean
-+/– above or below the mean
Example of variability in your everyday life
Calculating the IQR of test scores in a class to understand the range of scores and percentiles
