Mean for Grouped Data Mean = sum of weighted midpoints / n = 4650/100=46.5
Mean is the balancing point of the distribution 0123456789 X X X X X X X MEAN
Key Properties of the Mean Sum of the differences between the individual scores and the mean equals 0 sum of the squared differences between the individual scores and the mean equals a minimum value. The minimum value
Weaknesses of each measure of central tendency MODE: ignores all other info. about values except the most frequent one MEDIAN: ignores the LOCATION of scores above or below the midpoint MEAN: is the most sensitive to extreme values
Mode Mean Median Impacts of skewed distributions
Measures of Dispersion Poverty Households (%) in 2 suburbs by tract Less dispersion more dispersion
Range Highest value minus the lowest value problem: ignores all the other values between the two extreme values
Interquartile range Based on the quartiles (25th percentile and 75th percentile of a distribution) Interquartile range = Q 3 -Q 1 Semi-interquartile range = (Q 3 -Q 1 )/2 eliminates the effect of extreme scores by excluding them
Graphic representation: Box Plot Infant mortality rate AfricaAsia Latin America
Variance A measure of dispersion based on the second property of the mean we discussed earlier: minimum
Step 1: Calculate the total sum of squares around the mean
Step 2: Take an average of this total variation Why n-1? Rather than simply n??? The normal procedure involves estimating variance for a population using data from a sample. Samples, especially small samples, are less likely to include extreme scores in the population. N-1 is used to compensate for this underestimate.
Step 3: Take the square root of variance Purpose: expresses dispersion in the original units of measurement--not units of measurement squared Like variance: the larger the value the greater the variability
Coefficient of Variation (V) V = (standard deviation / mean) Value : To allow you to make comparisons of dispersion across groups with very different mean values or across variables with very different measurement scales.