quartiles,deciles,percentiles.ppt

quartiles,deciles and percentiles slides business statistics

1. QUARTILES,DECILES,PERCENTILES BUSINESS STATISTICS

2. PRESENTED BY: SYED SAIF UR REHMAN ROLL NO: 011 MBA 1 st 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 U ngroup data is : Q 3  = 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 : Q 3  = ¾(n + 1) th  Term. Q 3  = ¾(11 + 1) th  Term. Q 3  = ¾(12) th  Term. Q 3  = 9 th  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 ( Σ f/4 – c) = 6 + 2/111 (437/4 - 13) = 6 + 0.0180 (109.25 – 13) = 7.73 ANSWER

8. D ecile  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 typ e 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 ( Σ f/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 (50 Σ f/100 – c) = 8 + 2/182 [50(437)/100 - 124] = 8 + 0.0109 (218.5 – 124) = 9.03 ANSWER

16. THANK YOU!