; Consolidation Visit Moodle up edu ps
Documents
User Generated
Resources
Learning Center
Your Federal Quarterly Tax Payments are due April 15th

# Consolidation Visit Moodle up edu ps

VIEWS: 3 PAGES: 18

• pg 1
```									  Probabilistic and
Statistical Techniques
Lecture 6

Eng. Ismail Zakaria El Daour

2011
1
Probabilistic and Statistical Techniques

Chapter 2 (part 4)
Summarizing and Graphing Data

2
Probabilistic and Statistical Techniques

Measures of position
Definition
   z Score (or standardized value)
the number of standard deviations
that a given value x is above or below
the mean

3
Probabilistic and Statistical Techniques

Measures of Position z score

Sample                  Population
xx                          x
z                        z
s                               
Round z to 2 decimal places

4
Probabilistic and Statistical Techniques

Interpreting Z Scores

Whenever a value is less than the mean, its
corresponding z score is negative
Ordinary values:   z score between –2 and 2
Unusual Values:    z score < -2 or z score > 2

5
Probabilistic and Statistical Techniques

Percentiles
 A percentile provides information about how the
data are spread over the interval from the smallest
value to the largest value.

 Admission test scores for colleges and universities
are frequently reported in terms of percentiles.

6
Probabilistic and Statistical Techniques

Percentiles

   The pth percentile of a data set is a
value such that at least p percent of the
items take on this value or less and at
least (100 - p) percent of the items
take on this value or more.

7
Probabilistic and Statistical Techniques

Arrange the data in ascending order.

Compute index i, the position of the pth percentile.

i = (p/100)n

If i is not an integer, round up. The p th percentile
is the value in the i th position.

If i is an integer, the p th percentile is the average
of the values in positions i and i +1.

8
Probabilistic and Statistical Techniques

90th Percentile
i = (p/100)n = (90/100)70 = 63
Averaging the 63rd and 64th data values:
90th Percentile = (580 + 590)/2 = 585
425   430   430   435   435   435   435   435   440   440
440   440   440   445   445   445   445   445   450   450
450   450   450   450   450   460   460   460   465   465
465   470   470   472   475   475   475   480   480   480
480   485   490   490   490   500   500   500   500   510
510   515   525   525   525   535   549   550   570   570
575   575   580   590   600   600   600   600   615   615
9
Probabilistic and Statistical Techniques

Quartiles

   Quartiles are specific percentiles.
   First Quartile = 25th Percentile
   Second Quartile = 50th Percentile = Median
   Third Quartile = 75th Percentile

10
Probabilistic and Statistical Techniques

Definition
 Q1 (First Quartile) separates the bottom
25% of sorted values from the top 75%.
 Q2 (Second Quartile) same as the median;
separates the bottom 50% of sorted
values from the top 50%.
 Q3 (Third Quartile) separates the bottom
75% of sorted values from the top 25%.

11
Probabilistic and Statistical Techniques

Third Quartile
Third quartile = 75th percentile
i = (p/100)n = (75/100)70 = 52.5 = 53
Third quartile = 525
425   430    430   435   435   435   435   435      440   440
440   440    440   445   445   445   445   445      450   450
450   450    450   450   450   460   460   460      465   465
465   470    470   472   475   475   475   480      480   480
480   485    490   490   490   500   500   500      500   510
510   515    525   525   525   535   549   550      570   570
575   575    580   590   600   600   600   600      615   615
12
Probabilistic and Statistical Techniques

Quartiles

Q1, Q2, Q3
divide ranked scores into four equal parts
25%    25%   25% 25%

(minimum)
Q1 Q2 Q3      (maximum)

(median)

13
Probabilistic and Statistical Techniques

Some Other Statistics
 Interquartile Range (or IQR): Q3 - Q1
Q3 - Q1
 Semi-interquartile Range:
2
 Midquartile:        Q3 + Q1
2
 10 - 90 Percentile Range: P90 - P10
14
Probabilistic and Statistical Techniques

Definitions

    A boxplot is a graph of a data set that consists of
a line extending from the minimum value to the
maximum value, and a box with lines drawn at
the first quartile, Q1; the median; and the third
quartile, Q3.

15
Probabilistic and Statistical Techniques

Boxplots

16
Probabilistic and Statistical Techniques

17
18

```
To top