Page 185 - Data Science class 10
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4.5. QUARTILES
Quartiles are a type of percentile. They are a set of descriptive statistics. They summarise the central tendency and
variability of a dataset or distribution.
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• The first quartile (Q1, or the lowest quartile) is the 25 percentile, which means that 25% of the data falls below
the first quartile.
• The second quartile (Q2, or the median) is the 50 percentile, which means that 50% of the data falls below
th
the second quartile.
• The third quartile (Q3, or the upper quartile) is the 75 percentile, which means that 75% of the data falls below
th
the third quartile.
2 2 4 5 5 5 8 9 9 9 12
First quartile First quartile First quartile
(Q1 or lower quartile) (Q1 or lower quartile) (Q1 or lower quartile)
The first quartile is the median of all the values to the actual median's (Q2) left. Similarly, the third quartile is the
median of all the values to the actual median's (Q2) right.
4.5.1. Interquartile Range
By using the values of the quartiles, we can also calculate the interquartile range. An interquartile range is defined
as the measure of the middle 50% of the values when ordered from lowest to highest. The interquartile range can
be determined by subtracting the first quartile (Q1) from the third quartile (Q3).
IQR = Q3 – Q1
Where:
IQR = interquartile range
Q1 = 1 quartile or 25th percentile
st
Q3 = 3 quartile or 75th percentile
rd
Let us take the following 10 data points:
[20, 40, 60, 80, 100,120, 140, 160, 180, 200]
Here, as there are ten values (an even number of values), the median is halfway between the fifth & sixth data
values, which gives us 110 as the median, or Q2.
20 40 60 80 100 110 120 140 160 180 200
Q2
The first quartile or Q1 is the median of all the values to the left of Q2. So here, 60 is the middle number of numbers
to the left of the actual median (Q2).
The third quartile or Q3 is the median of all the values to the right of Q2. Thus here, 160 is the middle number of
numbers to the right of the actual median (Q2).
20 40 60 80 100 110 120 140 160 180 200
Q1 Q2 Q3
Data Merging 183

