1. Engineering Probability and Statistics - SE-205 -Chap 6By
S. O. Duffuaa

2. Lecture Objectives Sample and population Random sample
Type of data summarizes
Numerical summarizes
Diagrams and Tables
Graphical summarizes

3. Numerical Summarizes Sample mean X-bar Population mean µ
Sample variance S2
Population variance σ2

4. Range: Max X – Min X
COV = S/(X-bar)

5. Objective of the Lecture
Sample and population
Random sample
Stem-leaf diagram
The frequency distribution
Histogram

6. Population and Sample
Population is the totality of observations we are concerned with.
Example: All Engineers in the Kingdom,
All SE students etc.
Sample : Subset of the population
50 Engineers selected at random, 10 SE students selected at random.

7. Stem-And –Leaf Diagram
Each number xi is divided into two parts the stem consisting of one or two leading digits
The rest of the digits constitute the leaf.
Example if the data is 126 then 12 is stem
and 6 is the leaf.
What is the stem and leaf for 76

8. Data Table 1.1 Compressive Strength of 80 Aluminum Lithium Alloy

9. Stem-And-Leaf f Stem leaf frequency 7 6 1 8 7 1 9 7 1 10 5 1 2

10. Number of Stems Considerations
Stem Leaf

11. Stem number considerations
Stem leaf 6L 6U 7L 7U 8L 8U 9L
9U 5

12. Number of Stems Between 20 and 5
Roughly n where n number of data points

13. Percentiles
Pth percentile of the data is a value where at least P% of the data takes on this value or less and at least (1-P)% of the data takes on this value or more.
Median is 50th percentile. ( Q2)
First quartile Q1 is the 25th percentile.
Third quartile Q3 is the 75th percentile.

14. Percentile Computation : Example
Data : 5, 7, 25, 10, 22, 13, 15, 27, 45, 18, 3, 30
Compute 90th percentile.
1. Sort the data from smallest to largest
3, 5, 7, 10, 13, 15, 18, 22, 25, 27, 30, 45
2. Multiply 90/100 x 12 = 10.8 round it to to the next integer which is 11.
Therefore the 90th percentile is point # 11 which is 30.

15. Percentile Computation : Example
If the product of the percent with the number of the data came out to be a number. Then the percentile is the average of the data point corresponding to this number and the data point corresponding to the next number.
Quartiles computation is similar to the percentiles.

16. Inter-quartile range
Q3 – Q1

17. Cumulative Relative Frequency
Class Interval
(psi)
Tally
Frequency
Relative Frequency
Cumulative Relative Frequency
70 ≤ x < 90 || 2
0.0250
90 ≤ x < 110
||| 3
0.0375
0.0625
110 ≤ x < 130
|||| | 6
0.0750
0.1375
130 ≤ x < 150
|||| |||| |||| 14
0.1750
0.3125
150 ≤ x < 170
|||| |||| |||| |||| || 22
0.2750
0.5875
170 ≤ x <1 90
|||| |||| |||| || 17
0.2125
0.8000
190 ≤ x < 210
|||| |||| 10
0.1250
0.9250
210 ≤ x < 230
|||| 4
0.0500
0.9750
230 ≤ x < 250
1.0000

18. 2 5 20 15
Frequency 10 5 70 90
190
210
230
250
Compressive Strength (
psi )

20. Whisker extends to smallest data point within 1
Whisker extends to smallest data point within 1.5 interquartile ranges from first quartile
Whisker extends to largest data point within 1.5 interquartile ranges from third quartile
Third Quartile
First Quartile
Second Quartile
Outliers
Extreme Outliers
Outliers
1.5 IQR
1.5 IQR
IQR
1.5 IQR
1.5 IQR

21.
Strength

22. 120
110
100
Quantity Index 90 80 70 1 2 3
Plant