1. Measures of Central Tendency Chapter 4 Homework: 1, 2, 3, 5, 6, 13 Ignore parts with eye-ball estimation

2. 3 essential characteristics of distributions n Conveys most info for most distributions 1. Where is middle of distribution? 2. How wide is distribution? 3. What is shape of the distribution? ~

3. Central Tendency n Middle of distribution l measures: mode, median, mean n Portable & compact communication l further simplification of data l lose more detail n Which most appropriate? l Depends on level of measurement l intent of your communication ~

4. Mode n Most frequently occurring value l appropriate for any measurement level nominal, ordinal, interval/ratio ~

5. Computing the Mode n Frequency distribution l most frequently occurring value n Grouped frequency distribution l find interval with highest frequency l report midpoint e.g., interval: 150 to 160 report: (160 + 150)/2 = 155 n Methods may produce different results ~

6. Frequency Distribution X f 191 182 163 153 145 132 126 117 103 96 85 73 62 52 50 mode =11 Computing the Mode Grouped Frequency Distribution X f 19-20 1 17-18 2 15-16 6 13-14 7 11-1213 9-10 9 7- 8 8 5- 6 4 50 mode =

7. Grouped Frequency Distribution X f 81-100 1 61-80 3 41-60 4 21-40 9 1-20 2 mode =

8. Median n Midpoint of a data set values ½ smaller, ½ larger l appropriate for ordinal & interval/ratio NOT nominal ~

9. 10 20 30 40 50 60 70 80 90

10. 10 20 30 40 50 60 70 80 90 Average Daily Temperature ( o F)

11. Finding the Median 1. List all values from largest---> smallest if f=3, then list 3 times 2. Odd # entries median = middle value middle = (n + 1)/2 3. Even # entries = half way b/n middle 2 values ~

12. Finding the Median: odd # f X97531 X97531 f 2 1 3 2 11 9975553331199755533311 (n + 1)/2 =

13. Finding the Median: even # f X97531 X97531 f 2 1 3 12 997555333111997555333111 n /2 = (n /2) + 1 = median = Average middle 2 values

14. Mean n Average l value on X-axis l may not be actual value in data set n Computing the mean Sample meanPopulation mean

15. Reporting Central Tendency n Depends on level of measurement n Nominal: mode only appropriate n Ordinal: mode & median l not mean ---> uneven intervals n Interval/ratio: all 3 appropriate ~

16. Comparing the Measures n Normal distribution l all 3 coincide n Skewed will not be same values l greatest effect of mean less on median, least on mode l positive: mode -->median-->mean l negative: mean <--median<--mode