REPORTER : MARIA KATRINA S. MACAPAZ

ORGANIZING DATA USING:

•PERCENTILES•*QUARTILES•*DECILES

• *PERCENTILES-is a measure used to indicate the value below which a given percentage of observations fall• . Let us call this P=%.

• Example: (100-P)%.• - The 90 percentile is the value below

with 90 % of observations may be found.

• * PERCENTAGES:• Data Set: 1, 2,3,4,5• How many numbers are even?• Percentage= # meeting Characteristics of interest *100

total number of observations

Percentage= * 100=40%

PENCENTILE

• A value below which a certain percentage of observations lie.

• Data set: • 2,2,3,4,5,5,5,6,7,8,8,8,8,8,9,9,10,11,11,12• What is the percentile ranking of “10”?• Percentile rank of x= # of values below *100 nPercentile rank of ‘10’ = *100= 80%

• Data set: • 2,2,3,4,5,5,5,6,7,8,8,8,8,8,9,9,10,11,11,12• What Value Exist at the percentile ranking of

25%?

Value #= (n+1)Value # = (20 +1) = 5. 25There is no “5.25th”, so I take the average of the 5th & 6th values

to find what value exist at the 25th percentile. = 5

QUARTILES

QUARTILES

FINDING MEDIAN , Q1, Q2 in a short cut way:

• DATA SET: 2,8,5,3,10,6,7,9,1• ARRANGED ORDER: 1,2,3,5,6,7,8,9,10

1,2,3,5, 6, 7,8,9,10• MEDIAN

• = =2.5 = = 8.5

• Raw or Ungrouped data:• First arrange the given data in the incrasing

order and use the formula for and quartile deviation. Q.D is given by:

• Q.D = Where: () th item and () th item

Compute quartiles for the data given:25,18,30,8,15,5,10,35,40,45

• Arrange data: 5,8,10,15,18,25,30,35,40,45

• )th item=(th item=(2.75)th item=2nd item + () (3rd item- 2nd item)=8 + (10-8)==8 + x 2= 8+ 1.5=9.5

Arrange data: 5,8,10,15,18,25,30,35,40,45

• 3()th item=(th item

• =3x(2.75)th item• = (8.25)th item• =8th item + (9th item-8th item)• =35 + (40-35)• =35+ 1.25= 36.25• =36.25

QUARTILE DEVIATION

• Q.D= =______• Q.D=

• = 13.37

DECILES• The values which divide an array into ten

equal parts are called deciles. The first, second,…… ninth deciles by respectively. The fifth decile ( corresponds to median. The second, fourth, sixth and eighth deciles which collectively divide the data into five equal parts are called quintiles.

Deciles for Ungrouped Data:

• Deciles for ungrouped data will be calculated from the following formulae;

=value of (th item = Value of th item = Value of th item

For Example:We will calculate second, third and seventh deciles from the following array of data.

20 28 29 30 36 37 39 42 53 54

55 58 61 67 68 70 74 81 82 93

= Value of th item• = th item• =4.2th item from below• = The value of the 4th item is 30 and that of the 5th

item is 36. Thus the second decile is a value 0.2th of the way between 30 and 36. The fifth decile will be 30 + 6(0.2) = 31.2.

• Therefore, = 31.2.

= Value of th item• = th item• =6.3th item from below• The value of the 6th item is 37 and that of the 7th item

is 39. Thus the third decile is 0.3th of the way between 37 and 39. The third decile will be 37 + 2(0.3) = 37.6. Hence, = 37.6.

= Value of th item• = th item• =14.7th item from below• The value of the 14th item is 67 and that of the 15th

item is 68. Thus the 7th decile is 0.7th of the way between 67 and 68, which will be as 67 + 1(0.7) = 67.7. Therefore, = 67.7.

SO IF YOU WANT TO ORGANIZE YOUR DATA BY THE USE OF (PERCENTILES, QUARTILES, DECILES) JUST REMEMBER THE FOLLOWING EQUATIONS:

• Percentile rank of x= # of values below *100 n

Q.D = *Where: () th item and () th item*=value of (th item