The presentation is all about measures of central tendency and measures of positions. It shows also several illustrative examples for more understanding of the topic. Each term like mean , median and mode at the same time, quartiles, deciles and percentiles are also being defined. Each measures of central tendency and each measures of position are illustrate and provided with several examples.

1. MLQHS
Good
Morning
Class!

2. MATH 10
WEEK 1
QUARTER 4
Measures of
Position
OBJECTIVE
S
1. Definethefollowing
measuresof position:
quartiles,deciles,and
percentiles;
2. Illustratethefollowing
measuresof position:
quartiles,deciles,and
percentiles.
Lyn on me

3. MEDIAN
MODE
Measures of Central Tendency
MEAN

4. Measures of
Central Tendency
- is a quantitative
representation of the set
of data under investigation.

5. - is the most important, the
most useful, and the most
widely used
measure of central
tendency. I t is the average
of the dataset.
Mean

6. Mean
Given: 9, 6,10,10, 7

7. Median
- is the
middle value
in a set of
numbers.

8. Median
Given: 9, 6,10,10, 7
6,7, 9, 10, 10

9. Median =
6, 7, 9, 10,10, 11
Given: 9, 6,10,10, 7

10. Mode
- is the most
frequently appearing
number in the dataset.

11. Mode
Given: 9, 6,10,10, 7
6,7, 9, 10, 10

12. Measures of Position
- are numerical
measures that are used
to describe the standing
or location of an
observation relative to
the rest of the data.

13. Measures of Position
Quartiles
Deciles
Percentiles

14. Quartiles
- are points that divide a ranked
data into four equal parts. Each
set of data has three quartiles.

15. - is a number such that at most one-
fourth or 25% of the data are smaller
in value than Q1 and at most three-
fourths or 75% are larger.
First Quartile

16. FirstQuartile
Q1
Lower Quartile

17. For an ungrouped data,
the first quartile is the
entry in the data set,
where 𝑛 is the number of
observations in the data set.

18. Example
Consider the data set
A = {14, 23, 19, 36, 25, 45, 39}.
Find Q1.

19. 1. List the data in increasing order. Label
the positions of the numbers, if
necessary.
Given:
1st 2nd 3rd 4th 5th 6th 7th
14 19 23 25 36 39 45
14, 23, 19, 36, 25, 45, 39

20. 1st 2nd 3rd 4th 5th 6th 7th
14 19 23 25 36 39 45
2. Compute for Q1.
For 𝑸𝟏:
Locate the term.

21. 1st 2nd 3rd 4th 5th 6th 7th
14 19 23 25 36 39 45
Computing for →
Therefore, 19 is the first
quartile (Q1) which is exactly
the 2nd number in the list.

22. - is a number such that one-half
or 50% of the data are below
and above in value than Q2.
Second Quartile

23. SecondQuartile
Middle Quartile
Median
Q2

24. For an ungrouped data, the
second quartile is the
entry in the data set,
where 𝑛 is the number of
observations in the data set.

25. Example :
Consider the data set
A = {14, 23, 19, 36, 25, 45, 39}.
Find Q2.

26. 1. List the data in increasing
order. Label the positions of
the numbers, if necessary.
1st 2nd 3rd 4th 5th 6th 7th
14 19 23 25 36 39 45
Given:14, 23, 19, 36, 25, 45, 39

27. 2. Compute for Q2.
For 𝑸2:
Locate the term.
1st 2nd 3rd 4th 5th 6th 7th
14 19 23 25 36 39 45

28. 1st 2nd 3rd 4th 5th 6th 7th
14 19 23 25 36 39 45
Computing for →
Therefore, 25 is the second
quartile (Q2) which is exactly
the 4th number in the list.

29. is a number such that at most three-
fourths or 75% of the data are
smaller in value than Q3,,and at
most one- fourth or 25% are larger.
Third Quartile

30. Third Quartile
Q3
Upper Quartile

31. For an ungrouped data, the third
quartile is the entry in the
data set,
where 𝑛 is the number of
observations in the data set.

32. Example :
Consider the data set
A = {14, 23, 19, 36, 25, 45, 39}.
Find Q3.

33. 1. List the data in increasing
order. Label the positions of
the numbers, if necessary.
1st 2nd 3rd 4th 5th 6th 7th
14 19 23 25 36 39 45
Given:14, 23, 19, 36, 25, 45, 39

34. 2. Compute for Q3.
For 𝑸3:
Locate the term.
1st 2nd 3rd 4th 5th 6th 7th
14 19 23 25 36 39 45

35. 1st 2nd 3rd 4th 5th 6th 7th
14 19 23 25 36 39 45
Computing for →
Therefore, 39 is the third
quartile (Q3) which is exactly
the 6th number in the list.

36. Interquartile Range ( IQR )
- is the difference between
Q3 and Q1.

37. Example :
Consider the data set
A = {14, 23, 19, 36, 25, 45, 39}.
Find IQR.

38. Q1 = 19 and Q3 = 39
IQR = 39 - 19 = 20
1st 2nd 3rd 4th 5th 6th 7th
14 19 23 25 36 39 45

39. Deciles
- are nine score points which
divide a ranked data into ten
equal parts.

40. D6 D7 D8 D9
D1 D2 D3 D4 D5

41. Example:
Consider the data set
C= {6, 9, 8, 4, 11, 9, 7, 2, 5, 14}.
Find D3.

42. 1. Listthedatain increasingorder.
1st2nd 3rd 4th 5th 6th 7th 8th 9th 10th
2 4 5 6 7 8 9 9 11 14

43. Tocomputefor D3:
Locatethe position.
wherek =1,2,3...,9 and
n is the number of observation

44. =
1st2nd 3rd 4th 5th 6th 7th 8th 9th 10th
2 4 5 6 7 8 9 9 11 14
k=3
n=10

45. =
1st2nd 3rd 4th 5th 6th 7th 8th 9th 10th
2 4 5 6 7 8 9 9 11 14
betweenthe3rd and4th data 𝟓+𝟔
𝟐
=
𝟏𝟏
𝟐
=5.5
Therefore,D3=5.5

46. Percentiles
- are ninety-nine score
points which divide a
ranked data into 100
equal parts.

47. D6 D7 D8 D9
D1 D2 D3 D4 D5
P10 P20 P30 P40 P50 P60 P70 P80 P90
Q1 Q2 Q3
Pk =
𝑘(𝑛+1)
100

48. Example:
Consider the data set
C= {6, 9, 8, 4, 11, 9, 7, 2, 6, 14}.
Find P60.

49. 1. Listthedatain increasingorder.
1st2nd 3rd 4th 5th 6th 7th 8th 9th 10th
2 4 6 6 7 8 9 9 11 14

50. Tocomputefor P60:
Locatethe position.
wherek =1,2, 3, ..., 99 and
n is the number of observation
𝒌(𝒏 + 𝟏)
𝟏𝟎𝟎

51. =
1st2nd 3rd 4th 5th 6th 7th 8th 9th 10th
2 4 6 6 7 8 9 9 11 14
𝒌(𝒏+𝟏)
𝟏𝟎𝟎
𝟔𝟎(𝟏𝟎+𝟏)
𝟏𝟎𝟎
𝟔𝟎(𝟏𝟏)
𝟏𝟎𝟎
=
𝟔.𝟔
= =
𝟔𝟔𝟎
𝟏𝟎𝟎

52. =
1st2nd 3rd 4th 5th 6th 7th 8th 9th 10th
2 4 6 6 7 8 9 9 11 14
𝒌(𝒏+𝟏)
𝟏𝟎𝟎
(𝟔.𝟔)𝒕𝒉
𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝟔𝒕𝒉 𝒂𝒏𝒅𝟕𝒕𝒉 𝒅𝒂𝒕𝒂
𝟖+𝟗
𝟐
= 𝟖. 𝟓
P60 = 𝟖. 𝟓