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

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? ~

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 ~

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

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: ( )/2 = 155 n Methods may produce different results ~

Frequency Distribution X f mode =11 Computing the Mode Grouped Frequency Distribution X f mode =

Grouped Frequency Distribution X f mode =

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

Average Daily Temperature ( o F)

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 ~

Finding the Median: odd # f X97531 X97531 f (n + 1)/2 =

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

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

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 ~

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