Statistical parameters
A single value presents information of the whole sample.
Mode (Mo)



Value that exists most often in sample.
A good parameter when there exist only few possible values for the
variable.
Only parameter that can be defined for nominal data.
Example. Query: “Which party would you vote if the election was today?”
Mode = party that gets most votes.
Example. Sample = 0, 0, 1, 2, 4, 5, 6, 9, 12
Mode = 0 (appears twice)
Median (Md)


Midpoint of an ordered sample
Good parameter for ordinal variable
Example. Sample = 0, 0, 1, 2, 4, 5, 6, 9, 12
Median = 4
(midpoint = 5th value)
Example. Sample = 0, 0, 1, 2, 4, 5, 6, 7, 9, 12
Md = 4, or Md = 5, or Md = 4,5
(or even Md = 4.2365780268, if you insist)
Mean (average)
x

x
i
n
For interval or ratio variable.
Example. Sample = 0, 0, 1, 2, 4, 5, 6, 9, 12
x
0  0  1  2  4  5  6  9 12
 4,3
9
Range

[Min ; Max]
Example. Range of car speeds during 12:00 – 13:00 in a certain checkpoint
was 43 km/h – 109 km/h
Range width
Max – Min
Example
(Previous one) Range width = 109 – 43 = 66 km/h
Percentage points
p% -point: p% of values are BELOW p%-point. Based on number of values
only!
Example. 5% -point (or p5%) :
5% of values are below p5% and 95% of values are above p5%.
if n = 200 then 10 values would be below p5% and 190 values would be above
p5% .

Quartiles:
Q1 = 25% point
Q3 = 75% point

Deciles
D1 = 10% point
D2 = 20% point
∙∙∙
D9 = 90% point
Standard deviation (s)

Close to “Average of distances between a single value and Mean”
s

 x
i
x

2
n 1
Without mean:
 x 
x


n
2
i
2
s

i
n 1
“n-1” is used as divider to prevent us giving too small deviation (based
on a abnormally clean sample)
Two cases, when n can be used:
A: sample size ≤ 30
B: when we study the population (instead a sample)
Parameters with Excel
Mode
=MODE(array)
Median
=MEDIAN(array)
Mean
=AVERAGE(array)
Percentile (Pn%)
=PERCENTILE(array;p%)
Lowest value
=MIN(array)
Highest value
=MAX(array)
Standard deviation =STDEV(array)
=STDEVP(array)
[divider = n-1]
[divider = n]