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: (160 + 150)/2 = 155
Methods may produce different
results ~
6. Frequency Distribution
X f
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
mode = 11
Computing the Mode
Grouped
Frequency
Distribution
X f
19-20 1
17-18 2
15-16 6
13-14 7
11-12 13
9-10 9
7- 8 8
5- 6 4
50
mode =
10. 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 # f
X
9
7
5
3
1
f
2
1
3
3
2
11
9
9
7
5
5
5
3
3
3
1
1
(n + 1)/2 =
13. Finding the Median: even # f
X
9
7
5
3
1
f
2
1
3
3
3
12
9
9
7
5
5
5
3
3
3
1
1
1
n /2 =
(n /2) + 1 =
median =
Average middle 2 values
14. Mean
Average
value on X-axis
may not be actual value in data set
Computing the mean
Sample mean
n
X
X
Population mean
N
X
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
17. 10 20 30 40 50 60 70 80 90
mode
median
mean
10 20 30 40 50 60 70 80 90
mode
median
mean
10 20 30 40 50 60 70 80 90
mode
median
mean