UNGROUPED DATA

MEASURES OF POSITION

FOR UNGROUPED

DATA

UNGROUPED DATA

The ungrouped data has not been classified or has not been subdivided in the form of groups.

This type of data is totally the raw data. Ungrouped data is just in the form of number list. 

It is the data collected in original form. We can say that ungrouped data is an array of numbers.

Mean of Ungrouped Data

The mean is defined as the average value of the data. It is the value that is representative of all the values in a data set.

QUARTILE FOR UNGROUPED

DATA

QUARTILE

Values that divide a list of numbers into quarters.

1st Quartile = 25% of distribution.2nd Quartile = 50% of distribution.3rd Quartile = 75% of distribution.

8,10,15,13,3,6,4,12,9,7,5,1,11,2,14

1. Arrange the data from lowest to highest (ascending) order.

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15

N = 15 (total number of data set)Q1 = 4Q2 = 8Q3 = 12

USE THE FORMULA

Q1 = ¼(n+1)Q1 = ¼(15+1)Q1 = ¼(16)Q1 = ¼ x 16/1Q1 = 16/4Q1 = 4

Q2 = 2/4(n+1)Q2 = 2/4(15+1)Q2 = 2/4(16)Q2 = 2/4 x 16/1Q2 = 32/4Q2 = 8

Q3 = ¾(n+1)Q3 = ¾(15+1)Q3 = ¾(16)Q3 = ¾ x 16/1Q3 = 48/4Q3 = 12

ODD NUMBERS :

1, 2 , 3 , 4 , 5 Q1 Q2 Q3

EVEN NUMBERS :

1, 2 , 3 , 4 , 5 , 6

Q1 = 2.5 Q2 = 3.5 Q3 = 4.5

1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6

Q1 = 2.5Q2 = 3.5Q3 = 4.5

AVERAGE

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15FORMULA:Q2= Q1+Q3 = 4+12 = 16 = 8 2 2 2

RULESLOWER QUARITILE : Left side of the data set

Rounding up

UPPER QUARTILE : Right side of the data set

Rounding down

LINEAR INTERPOLATION

1, 27, 16, 7, 31, 7, 30, 3, 211, 3, 7, 7, 16, 21, 27, 30, 31 n=9

MENDENHALL METHOD

Qk = k/4(n+1)Q1 = ¼(n+1)Q1 = ¼(9+1)Q1 = 1/4(10)Q1 = ¼ x 10/1Q1 = 10/4Q1 = 2.5 or 3rd ( rounding up )Q1 = 7

INTERPOLATION METHOD

FORMULA: Higher value – Lower value

H=7 L=37 – 3 = 4 4(0.5)= 2Lower value + the product = Q13+2=5Q1 = 5

MENDENHALL : Q3 = 3/4(n+1)Q3 = ¾(9+1)Q3 = ¾(10)Q3 = ¾ x 10/1Q3 = 30/4Q3 = 7.5 or 7th ( rounding down )Q3 = 27

INTERPOLATION :

27 – 30 = 33(0.5) = 1.51.5+27 = 28.5Q3 = 28.5

DECILE FOR UNGROUPED

DATA

DECILEDividing the data set into 10 equal parts.

Mendenhall Formula : Decile Dj = j/10(n+1)Interpolation Formula : DecileDj = lower value + [decimal part (higher value – lower value)]

Ex. 6, 10, 18, 32, 13, 2, 3, 9, 34, 45

2, 3, 6, 9, 10, 13, 18, 32, 34, 45 n=10MENDENHALL METHOD: Dj = j/10(n+1)D3 = 3/10(10+1)D3 = 3/10(11)D3 = 3/10 x 11/1D3 = 33/10D3 = 3.3 or 3rd

D3 = 6

Interpolation:

Dj = Lower value+[Decimal part(higher value-lower value)]

D3 = 6+[0.3(9-6)]D3 = 6+[0.3(3)]D3 = 6+0.9D3 = 6.9

PERCENTILE FOR

UNGROUPED DATA

PERCENTILEThe percentiles are the ninety – nine score points

which divide a distribution into one hundred equal parts, so the each part represents the data set.

It is used to characterize values according to the percentage below them.

The 1st decile is the 10th percentile (P10). It means 10% of the data is less than or equal to the value of P10 or D1, and so on.

FORMULA :

Pk = k/100(n+1)

Sample Problem :

Find the 30th percentile of the following test scores of a random sample of ten students: 35, 42, 40, 28, 15, 23, 33, 20, 18, 28

Arrange the scores/data from the lowest to highest (ascending) order.

15, 18, 20, 23, 28, 28, 33, 35, 40, 42Then use the formula :Pk=k(n+1) 100

P30 = 30(10+1) 100P30 = 30(11) 100P30 = 330/100P30 = 3.3 or 3rd P30 = 20