1. DESCRIBING DATA: 2

2. Numerical summaries of data using measures of central tendency and dispersion

3. Central tendency--Mode Table 1. Undergraduate Majors

4. Bimodal Distributions Table 1. Undergraduate Majors

5. Mode for Grouped Frequency Distributions based on Interval Data Midpoint of the modal class interval

6. Median The point in the distribution above which and below which exactly half the observations lie (50th percentile) Calculation depends on whether the no. of observations is odd or even.

7. Median= 188

8. MEDIAN for grouped frequency distributions based on interval data Median = 40 + ((20/30) * 10) = 40 + 6.67 = 46.67

9. ARITHMETIC MEAN

10. Mean for Grouped Data Mean = sum of weighted midpoints / n = 4650/100=46.5

11. Mean is the balancing point of the distribution 0123456789 X X X X X X X MEAN

12. 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

13. 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

14. Mode Mean Median Impacts of skewed distributions

15. Measures of Dispersion Poverty Households (%) in 2 suburbs by tract Less dispersion more dispersion

16. Range Highest value minus the lowest value problem: ignores all the other values between the two extreme values

17. 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

18. Graphic representation: Box Plot Infant mortality rate AfricaAsia Latin America

19. Variance A measure of dispersion based on the second property of the mean we discussed earlier: minimum

20. Step 1: Calculate the total sum of squares around the mean

21. 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.

22. 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

23. 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.