Powerpoint presentation

2. MREAUSE
MEASURE

3. PISTOION
POSITION

4. IDEVID
DIVIDE

5. UQALE
EQUAL

6. MEASURES OF POSITION
with Computer Application

7. OBJECTIVES
•Define measures of position
•Illustrate the following measures of
position:
–Quartiles
–Deciles
–Percentiles

8. NUMERICAL INFORMATION MAY BE
CLASSIFIED AS:
•Ungrouped data
•Grouped data

10. MEASURES OF POSITION/QUANTILES
- are techniques that divide a
set of data into equal groups
Fractiles are numbers that partition or
divide an ordered data set into equal parts.

11. MEASURES OF POSITION/QUANTILES
•Used to describe the position
of a data value in relation to
the rest of the data.
Types:
1. Quartiles
2. Percentiles
3. Deciles

12. QUANTILES CAN BE APPLIED WHEN:
•Dealing with large amount of data,which
includes the timely results for standardized
tests in schools,etc.
•Trying to discover the smallest as well as the
largest values in a given distribution.
•Examining financial fields for academic as well
as statistical studies.

13. MEASURES OF
POSITION FOR
UNGROUPED DATA
Q U A R T I L E , D E C I L E A N D P E R C E N T I L E

14. QUARTILE
U N G R O U P E D D A T A B Y I N S P E C T I O N

15. QUARTILE FOR UNGROUPED DATA
•The quartiles are the score points
which divide a distribution into
four equal parts.

16. Quartiles

17. Q1, Q2, Q3
Quartiles

18. Q1, Q2, Q3
divides ranked scores into four equal parts
Quartiles

19. Q1, Q2, Q3
divides ranked scores into four equal parts
Quartiles
25% 25% 25% 25%
Q1 Q2 Q3

20. Q1 – LOWER QUARTILE
At most,25% of data is smaller than
Q1.
It divides the lower half of a data
set in half.

21. Q2 – MIDDLE QUARTILE
•The median divides the data set in
half.
•50% of the data values fall below
the median and 50% fall above.

22. Q3 – UPPER QUARTILE
•At most,25% of data is larger than
Q3.
•It divides the upper half of the
data set in half.

23. Q1 Q2 Q3
25% 25% 25% 25%

24. QUARTILE
U N G R O U P E D D A T A B Y M E N D E N H A L L
A N D S I N C I C H M E T H O D

25. MENDENHALL AND SINCICH METHOD :
A METHOD OF FINDING THE QUARTILE VALUE
• This method is being developed byWilliam Mendenhall andTerry
Sincich to find the position of the quartile in the given data.

26. MENDENHALL AND SINCICH METHOD :
A METHOD OF FINDING THE QUARTILE VALUE
• Formula:
Lower Quartile (L) = Position of Q1= ¼ (n+1)
Q2= 2(n+1) = n+1 th observation
2
Upper Quartile (U) = Position of Q3 = ¾ (n+1)
4

27. MENDENHALL AND SINCICH METHOD :
A METHOD OF FINDING THE QUARTILE VALUE
• N is the number of elements in the data
Example:The manager of a food chain recorded the number of
customers who came to eat the products in each day.The results
were 10,15,14,13,20,19,12 and 11.
• In this example N=8

28. MENDENHALL AND SINCICH METHOD
A METHOD OF FINDING THE QUARTILE VALUE
1. CALCULATE THE POSITION OF THE LOWER QUARTILE
4
Lower Quartile (L) = Position of Q1 = 1
(n +1)

29. MENDENHALL AND SINCICH METHOD
A METHOD OF FINDING THE QUARTILE VALUE
2. CALCULATE THE POSITION OF THE UPPER QUARTILE
4
Upper Quartile (U) = Position of Q3 = 3
(n +1)

30. MENDENHALL AND SINCICH METHOD
A MET HOD OF FINDING THE QUAR TILE VAL UE
4
Position of Q1 = 1
(n +1)
= 1
(9 +1)
4
= 2.5 (round up)
= 3
THELOWER QUARTILEVALUEQ1 IS THE 3RD DATAELEMENT, SO Q1 = 5
4
1
(n +1) and round off to the nearest integer.
EXAMPLE DATA SET
{1, 3, 5 7, 16, 21, 27, 30, 31} and n = 9
To find Q1 locate its position using the formula

31. MENDENHALL AND SINCICH METHOD
A MET HOD OF FINDING THE QUAR TILE VAL UE
4
Position of Q3 = 3
(n +1)
= 3
(9 +1)
4
= 7.5(round down)
= 7
THEUPPER QUARTILEVALUEQ3 IS THE7TH DATAELEMENT, SO Q3 = 27
4
3
(n +1) and round off to the nearest integer.
EXAMPLE DATA SET
{1, 3, 5, 7, 16, 21, 27, 30, 31} and n = 9
To find Q3 locate its position using the formula

32. DECILES

37. PERCENTILES

41. MEASURES OF POSITION
with Computer Application