This document defines and discusses quartiles, deciles, and percentiles. Quartiles divide a data set into four equal parts, with the first quartile (Q1) representing the lowest 25% of values. Deciles divide data into ten equal parts. Percentiles indicate the value below which a certain percentage of observations fall. Examples are provided for calculating Q1, Q3, D1 using formulas for grouped and ungrouped data sets. Quartiles, deciles, and percentiles are commonly used to summarize and report on statistical data.

1. QUARTILES,DECILES,PERCENTILES
BUSINESS STATISTICS

2. PRESENTEDBY:
SYED SAIF UR REHMAN
ROLL NO: 011
MBA 1st SEMESTER

3. DEFINE QUARTILE?
“Quartiles in statistics are values that divide your data into
quarters”. However, quartiles aren’t shaped like pizza slices; Instead
they divide your data into four segments according to where the
numbers fall on the number line. The four quarters that divide a data
set into quartiles are:
 The lowest 25% of numbers.
 The next lowest 25% of numbers (up to the median).
 The second highest 25% of numbers (above the median).
 The highest 25% of numbers.

4. USES OF QUARTILES
• Quartiles are used to summarize a group of numbers.
• Instead of looking a big list of numbers(we look at just few
numbers that gives us a picture of whats going on in the big list).
• Are great for reporting on a set of data and for making box and
whisker plots.
• Especially useful when you’re working with data that is not
symmetrically distributed or a data set that has outliers.
• Quartile summary is also play an important role in
benchmarking.

5. The upper quartile formula for Ungroup data is:
Q3 = ¾(n + 1)th Term.
The formula doesn’t give you the value for the upper quartile, it gives you
the place. For example, the 5th place, or the 76th place.
PROBLEM: Put your numbers in order: 1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.
SOLUTION:
Work the formula. There are 11 numbers in the set, so:
Q3 = ¾(n + 1)th Term.
Q3 = ¾(11 + 1)th Term.
Q3 = ¾(12)th Term.
Q3 = 9th Term.
In this set of numbers (1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27), the upper quartile
(18) is the 9th term, or the 9th place from the left.
Examples of Quartile for Ungroup and Group data:

6. Age Number C.F
4-6 13 13
6-8 111 124
8-10 182 306
10-12 105 411
12-14 19 430
14-16 7 437
437
PROBLEM: Find Q1 using the following data set.

7. SOLUTION:
For group data formula:
Q1 = l + h/f (Σf/4 – c)
= 6 + 2/111 (437/4 - 13)
= 6 + 0.0180 (109.25 – 13)
= 7.73 ANSWER

8. Decile is any of the nine values that divide the
sorted data into ten equal parts, so that each part
represents 1/10 of the sample or population.
DEFINE DECILE?

9. USES OF DECILES
 It makes easy to discover the smallest as well as largest values
of the given distribution.
 It is very useful when dealing with large amounts of data,which
includes the timely results for standardized tests in schools etc.
 It helps Govt. to find how the income in a country is
distributed,how much of the total income is earned by low wage
earning groups and by high wage earning groups.
 This type of grouping can be mostly seen in financial fields for
academical as well as statistical studies.

10. PROBLEM: Find D1 using the following data set.
Age Number C.F
4-6 13 13
6-8 111 124
8-10 182 306
10-12 105 411
12-14 19 430
14-16 7 437
437

11. SOLUTION:
For group data formula:
D1 = l + h/f (Σf/10 – c)
= 6 + 2/111 (437/10 - 13)
= 6 + 0.0180 (43.7 – 13)
= 6.55 ANSWER

12. A percentile (or a centile) is a measure used
in statistics indicating the value below which a given percentage of
observations in a group of observations falls.
DEFINE PERCENTILE?

13. USES OF PERCENTILES:
• PERCENTILES are used to understand and interpret data. They
indicate the values below which a certain percentage of the
data in a data set is found.
• Percentiles are frequently used to understand test scores and
biometric measurements.
• Percentiles are used extensively to report scores in academic
exams and tests such as GAT,NTS etc.

14. Age Number C.F
4-6 13 13
6-8 111 124
8-10 182 306
10-12 105 411
12-14 19 430
14-16 7 437
437
PROBLEM: Find D1 using the following data set.

15. SOLUTION:
For group data formula:
P50 = l + h/f (50Σf/100 – c)
= 8 + 2/182 [50(437)/100 - 124]
= 8 + 0.0109 (218.5 – 124)
= 9.03 ANSWER

16. THANKYOU!