MEASURE OF POSITION!
Remember that the median is
the value where 50% of the
Imagine quantitative data like academic
distribution falls or lies above it
performances (you can have your
while 50% lies below it.
grades) or height that can be arranged
in ascending order. By analysing the So basically we define fractiles
height of students, for instance, one can or quantiles based on how they
say that he performed better than 50% equally divide a distribution.
of his class or that he is smaller than
25% of his classmates. Quartiles- the values that divide a rank-
ordered into 4 equal parts.
Deciles- the values that divide a rank-
Measure of position- ordered data set into 10 equal parts.
- Determines the position of a Percentile- the values that divide a
single value in relation to other rank-ordered data set into 100 equal
values in sample or population parts.
data set.
- are quantities which locate QUARTILES
values in a data set.
Quartiles- the values that divide a rank-
- Indicate the location of a certain ordered into 4 equal parts.
computed value from a
25 25 25 25
distribution. It gives you the
opportunity to identify if the value
is the border line of one set of - First quartile (𝑄1) is value such
scores from the other or how that at most one-fourth or 25% of
much value it surpassed or how the data are lower than 𝑄1 , at
much value had surpassed. most three-fourths or 75% are
greater than 𝑄1. It is also called
The measure of central tendency
as the lower quartile.
refer only to the center of the entire set
of data. There are other measures of - Second quartile (𝑄2 ) is a value
location that describe or locate the non- such that at most one-half or
central position. These measures are 50% of the data are lower than
called to as fractiles or quantiles 𝑄2 , and at most one half or 50%
are greater than 𝑄2 . It is also
Fractiles or quantiles
known as the median or the
When the data is arranged in lower quartile.
ascending or descending order,
- Third quartile (𝑄3 ) is a value that
values can be determined so
at most three-fourths or 75% of
that the data is divided into
the data are lower than 𝑄3 , and
several equal parts is called
at most one-fourth or 25% are
fractiles or quantiles. One of
greater than 𝑄3 . It is also called
the quantiles is the median.
as the upper quartile.
𝑄1 < 𝑄2 < 𝑄3
Interquartile range- is the difference (Using the formula)
between 𝑄3 - 𝑄1
Mendenhall and Sincich Method
using statistics for engineering and the
sciences, define a different method of
finding quartile values.
𝑄1 𝑄2 𝑄3 Given:
n = 11
Example:
Solution:
The owner of a coffee shop recorded
the number of customers who came 5,8,9,9,10,10,11,12,14,14,17
into his café each hour in a day. The 𝒊
results were 14, 𝑸𝒊 = ( 𝒏 + 𝟏)
𝟒
10,12,9,17,5,8,9,14,10, and 11. Find
the lower quartile and upper quartile.
(Without using the formula) a. Find the lower quartile or 𝑄1
Solution: 𝟏
𝑸𝟏 = ( 𝟏𝟏 + 𝟏)
𝟒
Step 1: Arrange the data in ascending 12
order 𝑸𝟏 = 4
5,8,9,9,10,10,11,12,14,14,17 𝑸𝟏 = 3
Step 2: Determine the middle value. Thus, the lower quartile is at the 3rd
observation.
5,8,9,9,10,10,11,12,14,14,17
5,8,9,9,10,10,11,12,14,14,17
Therefore, the median or the middle
quartile 𝑸𝟐 is 10. b. Find the median or middle
quartile.
Step 3: Determine the lower quartile
that is between the middle value and 𝟐
𝑸𝟐 = ( 𝟏𝟏 + 𝟏)
the least value in the data set. 𝟒
5,8,9,9,10,10,11,12,14,14,17 𝟐𝟒
𝑸𝟐 = ( )
𝟒
Therefore, the lower quartile or 𝑸𝟏 is
9. 𝑸𝟐 = 𝟔
Step 4: Determine the upper quartile
that is between the middle value and Thus, the middle quartile is at the 6th
the greatest value in the data set. observation.
5,8,9,9,10,10,11,12,14,14,17 5,8,9,9,10,10,11,12,14,14,17
Therefore, the upper quartile or 𝑸𝟑 c. Find the upper quartile.
is 14.
𝟑
𝑸𝟑 = ( 𝟏𝟏 + 𝟏)
𝟒
𝟑𝟔 𝑸𝟑 = 𝟕. 𝟓
𝑸𝟑 = ( )
𝟒
𝑸𝟑 = 𝟗
Therefore, the computed value 7.5
Thus, the middle quartile is at the becomes 7 after rounding down.
9th observation. The upper quartile value is 𝑄3 is the
5,8,9,9,10,10,11,12,14,14,17 7th element, so 𝑄3 = 27.
Formula for Quartile
𝒊
𝑸𝒊 = (𝒏 + 𝟏)
𝟒
Where
i= 1,2,3 (Quartile)
n = number or sample
Example 2:
Given set:
1, 3,7,7,16,21,27,30,31
a. Find the Lower quartile (L)
1
Position of 𝑄1 = 4 (9 + 1)
1
𝑄1 = (9 + 1)
4
1
𝑄1 = (10)
4
𝑄1 = 2.5
Therefore, 2.5 becomes 3 after
rounding up. The lower quartile
value 𝑄1 is the 3rd observation, so 𝑄1 =
7.
b. Find the upper quartile (U)
3
𝑄3 = (9 + 1)
4
3
𝑄3 = (10)
4
