This document discusses measures of central tendency and dispersion for ungrouped data, including the mean, quartiles, deciles, and percentiles. It provides formulas for calculating these values and examples worked out step-by-step. The mean is defined as the average value of the data. Quartiles divide the data into four equal parts, with the first quartile being the 25th percentile, second quartile the 50th percentile (median), and third quartile the 75th percentile. Deciles and percentiles further divide the data into 10 and 100 equal parts, respectively, using formulas that calculate the cutoff points.

1. UNGROUPED
DATA

2. MEASURES OF
POSITION
FOR UNGROUPED
DATA

3. 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.

4. 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.

5. QUARTILE FOR
UNGROUPED
DATA

6. 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.

7. 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.

8. 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
N = 15 (total number of data set)
Q1 = 4
Q2 = 8
Q3 = 12

9. USE THE FORMULA
Q1 = ¼(n+1)
Q1 = ¼(15+1)
Q1 = ¼(16)
Q1 = ¼ x 16/1
Q1 = 16/4
Q1 = 4

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

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

12. ODD NUMBERS :
1, 2 , 3 , 4 , 5
Q1 Q2 Q3

13. EVEN NUMBERS :
1, 2 , 3 , 4 , 5 ,
6
Q1 = 2.5 Q2 = 3.5 Q3 = 4.5

14. 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6
Q1 = 2.5
Q2 = 3.5
Q3 = 4.5

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

16. RULES
LOWER QUARITILE : Left side of the data
set
Rounding up
UPPER QUARTILE : Right side of the data
set
Rounding down

17. LINEAR INTERPOLATION
1, 27, 16, 7, 31, 7, 30, 3, 21
1, 3, 7, 7, 16, 21, 27, 30, 31 n=9

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

19. INTERPOLATION METHOD
FORMULA: Higher value – Lower value
H=7 L=3
7 – 3 = 4
 4(0.5)= 2
Lower value + the product = Q1
3+2=5
Q1 = 5

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

21. INTERPOLATION :
27 – 30 = 3
3(0.5) = 1.5
1.5+27 = 28.5
Q3 = 28.5

22. DECILE FOR
UNGROUPED
DATA

23. DECILE
Dividing the data set
into 10 equal parts.

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

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

26. Interpolation:
 Dj = Lower value+[Decimal part(higher
value-lower value)]
D3 = 6+[0.3(9-6)]
D3 = 6+[0.3(3)]
D3 = 6+0.9
D3 = 6.9

27. PERCENTILE FOR
UNGROUPED
DATA

28. PERCENTILE
 The 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.

29. FORMULA :
Pk = k/100(n+1)

30. 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

31. Arrange the scores/data from the lowest to
highest (ascending) order.
15, 18, 20, 23, 28, 28, 33, 35, 40, 42
Then use the formula :
Pk=k(n+1)
100

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