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

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

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

6. Computing the Mode mode = 11 mode = X f Grouped Frequency Distribution
19 1
18 2
16 3
15 3
14 5
13 2
12 6
11 7
10 3
9 6
8 5
7 3
6 2
5 2 50
Grouped
Frequency
Distribution
X f 50
mode =

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

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

9. 10 20 30 40 50 60 70 80 90

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

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 # f9 7 5 3 1 X 9 7 5 3 1 f 2 1 3 11
(n + 1)/2 =

13. Finding the Median: even # f9 7 5 3 1 X 9 7 5 3 1 f 2 1 3 12
Average middle 2 values
median =
n /2 =
(n /2) + 1 =

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

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

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