The document discusses quartiles, which divide a data set into four equal parts. The first quartile contains the smallest 25% of values, the second quartile contains values between the 25th and 50th percentiles, the third quartile contains values between the 50th and 75th percentiles, and the fourth quartile contains the largest 25% of values. Formulas are provided for calculating the lower quartile (Q1), median (Q2), and upper quartile (Q3). The quartile deviation is defined as half the distance between Q3 and Q1, while the interquartile range is the full distance between Q3 and Q1. Examples are given to illustrate quartile calculations.

1. EDUCATIONAL STATISTICS
QUARTILE
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2. IN STATISTICS, A QUARTILE IS A TYPE OF QUANTILE WHICH
DIVIDES THE NUMBER OF DATA POINTS INTO FOUR PARTS,
OR QUARTERS, OF MORE-OR-LESS EQUAL SIZE
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3. 1. First quartile: 25% from smallest to
largest of numbers
2. Secondquartile: between 25.1% and
50% (till median)
3. Third quartile: 51% to 75% (above the
median)
4. Fourth quartile: 25% of largest numbers
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4. DIVISION OF QUARTILE
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5. CALCULATING LOWER, MIDDLE, & UPPER QUARTILE
 Q1 = [(n+1)/4]th item
 Q2 = [(n+1)/2]th item
 Q3 = [3(n+1)/4]th item
Hence, the formula for quartile can be given by;
Where, Qr is the rth quartile
l1 is the lower limit
l2 is the upper limit
f is the frequency
c is the cumulative frequency of the class preceding the quartile
class.
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6. QUARTILE FOR GROUPED DATA
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7. Example 1
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8. Example 2
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9. Example 3
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10. QUARTILE DEVIATION
 You have learned about standard deviation in statistics. Quartile deviation is defined as half
of the distance between the third and the first quartile. It is also called Semi Interquartile
range. If Q1 is the first quartile and Q3 is the third quartile, then the formula for deviation is
given by;
 Quartile deviation = (Q3-Q1)/2
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11. INTERQUARTILE RANGE
 The interquartile range (IQR) is the difference between the upper and lower quartile of a
given data set and is also called a midspread. It is a measure of statistical distribution, which
is equal to the difference between the upper and lower quartiles. Also, it is a calculation of
variation while dividing a data set into quartiles. If Q1 is the first quartile and Q3 is the third
quartile, then the IQR formula is given by;
 IQR = Q3 – Q1
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12. Dr. Hina Jalal
@AksEAina (hinansari23@gmail.com)