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7 - Quantiles or Fractiles

Quartiles divide a list of numbers into four equal parts. To calculate quartiles, the numbers are first ordered from lowest to highest value. The list is then cut into four equal sections with the quartile values at the cut points. The first quartile (Q1) is the middle number of the lower half of the list and the third quartile (Q3) is the middle number of the upper half. The interquartile range is calculated by subtracting Q1 from Q3. Deciles divide a list into ten equal parts instead of four. Percentiles indicate the percentage of values that are equal to or below a given value.

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150 views24 pages

7 - Quantiles or Fractiles

Quartiles divide a list of numbers into four equal parts. To calculate quartiles, the numbers are first ordered from lowest to highest value. The list is then cut into four equal sections with the quartile values at the cut points. The first quartile (Q1) is the middle number of the lower half of the list and the third quartile (Q3) is the middle number of the upper half. The interquartile range is calculated by subtracting Q1 from Q3. Deciles divide a list into ten equal parts instead of four. Percentiles indicate the percentage of values that are equal to or below a given value.

Uploaded by

Angel Rosales
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PPTX, PDF, TXT or read online on Scribd
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QUANTILE OR

FRACTILES
QUARTILE
What is Quartile?
 Quartiles are the values that
divide a list of numbers into
quarters:
 Put the list of numbers in order
 Then cut the list into four

equal parts
 The Quartiles are at the "cuts"
What is Quartile?
Example: 5, 7, 4, 4, 6, 2, 8
 Put them in order: 2, 4, 4, 5, 6, 7, 8
 Cut the list into quarters:
What is Quartile?
 And the result is:

Quartile 1 (Q1) = 4


Quartile 2 (Q2), which is also the Median, = 5
Quartile 3 (Q3) = 7
What is Quartile?
Example:1, 3, 3, 4, 5, 6, 6, 7, 8, 8
 The numbers are already in order
 Cut the list into quarters:

In this case Quartile 2 is half way between 5 and 6:

Q2 = (5+6)/2 = 5.5
What is Quartile?
 And the result is:

Quartile 1 (Q1) = 3


Quartile 2 (Q2) = 5.5
Quartile 3 (Q3) = 7
Interquartile Range
The "Interquartile Range" is from Q1 to Q3:

To calculate it just subtract Quartile


1 from Quartile 3
Interquartile Range
 The Interquartile Range is:

Q3 − Q1 = 7 − 4 = 3
DECILE
What is Decile
 Deciles are similar to quartiles. But while
quartiles sort data into four quarters, deciles
sort data into ten equal parts: The 10th, 20th,
30th, 40th, 50th, 60th, 70th, 80th, 90th and
100th percentiles.
Quartiles Deciles
Q1 = P25 D1 = P10

Q2 = P50 D2 = P20
Q3 = P75 D3 = P30
•
•
•
D =P
PERCENTILE
What is Percentile?
 A measure of position that divides the
ordered observations or score distribution
into 100 equal parts
What is Percentile?
Example: You are the fourth tallest person in a
group of 20

80% of people are shorter than you:


What is Percentile?
That means you are at the 80th percentile.

If your height is 1.85m then "1.85m" is the


80th percentile height in that group.
Estimating Percentiles
 We can estimate percentiles from a line graph
.
Estimating Percentiles
Example: Shopping

A total of 10,000 people visited the shopping


mall over 12 hours:
Estimating Percentiles
 a) Estimate the 30th percentile (when 30% of
the visitors had arrived).

 b) Estimate what percentile of visitors had


arrived after 11 hours.
Estimating Percentiles
First draw a line graph of the data: plot the
points and join them with a smooth curve:

a) The 30th
percentile occurs
when the visits
reach 3,000.
Estimating Percentiles
Draw a line horizontally across from 3,000
until you hit the curve, then draw a line
vertically downwards to read off the time on
the horizontal axis:

So the 30th
percentile occ
urs after
about 6.5
hours.
Estimating Percentiles
b) To estimate the percentile of visits after 11 hours:
draw a line vertically up from 11 until you hit the
curve, then draw a line horizontally across to read
off the population on the vertical axis:

So the visits at 11


hours were about
9,500, which is
the 95th
percentile.
Class Frequency Classmark fXm Cumulative
Interval (C.I) (fi) Xm frequency
(<cf)
74 – 81 2 77.5 50
66 – 73 4 69.5 48
58 – 65 8 61.5 44
50 – 57 10 53.5 36
42 – 49 11 45.5 26
34 – 41 8 37.5 15
26 – 33 4 29.5 7
18 - 25 3 21.5 3
N=50
Class Frequency Cumulative
Interval (C.I) (fi) frequency
(<cf)
90– 94 4
85 – 89 3
80 – 84 8
75 – 79 20
70 – 74 15
65 – 69 7
60 – 64 2
55 - 59 1
N=

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