Quartile (ungrouped)

Quartile (ungrouped)

1. MEASURES OF POSITION FOR UNGROUPED DATA: QUARTILES , DECILES , & PERCENTILES

2. Quartiles for ungrouped data The QUARTILES are the score points which divide a distribution into four equal parts. Q1 Q2 Q3 25% of the data has a value ≤ Q1 50% of the data has a value ≤ Q2 75% of the data has a value ≤ Q3

3. Quartiles for ungrouped data Q1 is called the LOWER QUARTILE Q2 is nothing but the MEDIAN Q3 is the UPPER QUARTILE

4. MENDENHALL AND SINCICH METHOD : A METHOD OF FINDING THE QUARTILE VALUE This method is being developed by William Mendenhall and Terry Sincich to find the position of the quartile in the given data.

5. MENDENHALL AND SINCICH METHOD : A METHOD OF FINDING THE QUARTILE VALUE Formula: Lower Quartile (L) = Position of Q1= ¼ (n+1) Q2= 2(n+1) = n+1 th observation 4 2 Upper Quartile (U) = Position of Q3 = ¾ (n+1)

6. MENDENHALL AND SINCICH METHOD : A METHOD OF FINDING THE QUARTILE VALUE N is the number of elements in the data Example: The manager of a food chain recorded the number of customers who came to eat the products in each day. The results were 10,15,14,13,20,19,12 and 11. In this example N=8

7. MENDENHALL AND SINCICH METHOD : A METHOD OF FINDING THE QUARTILE VALUE Q1= n+1 th observation 4 Q2= 2(n+1) = n+1 th observation 4 2 Q3= 3(n+1) th observation 4

8. MENDENHALL AND SINCICH METHOD : A METHOD OF FINDING THE QUARTILE VALUE Steps to solve the quartile of the given data 1. Arrange the data in ascending order or from the lowest value to the highest value. 2. Find the N or the total number of elements presented in the data. 3. Find the least value of the data and the greatest value of the data. 4. find the lower quartile of the given data using the Mendenhall & Sincich Method. Lower Quartile (L) = Position of Q1= ¼ (n+1)

9. MENDENHALL AND SINCICH METHOD : A METHOD OF FINDING THE QUARTILE VALUE 5. Find the middle value of the data or the Median. Use this formula Q2= 2(n+1) = n+1 th observation 4 2 6. Find the upper quartile of the given data. Use this formula Upper Quartile (U) = Position of Q3 = ¾ (n+1)

10. MENDENHALL AND SINCICH METHOD : A METHOD OF FINDING THE QUARTILE VALUE Example: The owner of the coffee shop recorded the number of customers who came into his café each hour in a day. The results were 14, 10, 12, 9, 17, 5, 8, 9, 14, 10, and 11.

11. MENDENHALL AND SINCICH METHOD : A METHOD OF FINDING THE QUARTILE VALUE Solution Ascending order {5, 8, 9, 9, 10, 10, 11, 12, 14, 14, 17} N=11 Least value= 5 Greatest value= 17

12. MENDENHALL AND SINCICH METHOD : A METHOD OF FINDING THE QUARTILE VALUE Lower Quartile (L) = Position of Q1= ¼ (n+1) Q1= ½ (n+1) Q1= ½ (11+1) Q1= ½ (12) Q1= 12/4 (divide) Q1= 3 {5, 8, 9, 9, 10, 10, 11, 12, 14, 14, 17} Therefore the Q1 is the 3 rd element in the data which is 9

13. MENDENHALL AND SINCICH METHOD : A METHOD OF FINDING THE QUARTILE VALUE Median Value or the middle value Q2= 2/4 (n+1) = n+1/2 th observation Q2= 2/4 (11+1) Q2= 2/4 (12) Q2= 24/4 Q2= 6 {5, 8, 9, 9, 10, 10, 11, 12, 14, 14, 17} Therefore the Q2 is the 6 th element in the data which is 10

14. MENDENHALL AND SINCICH METHOD : A METHOD OF FINDING THE QUARTILE VALUE Upper Quartile (U)= Position of Q3= ¾ (n+1) Q3= ¾ (11+1) Q3= ¾ (12) Q3= 36/4 Q3= 9 {5, 8, 9, 9, 10, 10, 11, 12, 14, 14, 17} Therefore the Q3 is the 9 th element in the data which is 14

15. Linear interpolation A method of finding the quartile value. Is a method of constructing new data points within the range of a discrete set of known data points. It is often required to interpolate, i.e., estimate the value of that function for an intermediate value of the independent variable. We need to use the interpolation if the value of the position is in decimal form.

16. Linear interpolation Using the formula Qk = k/4 (n+1) k= position of the quartile n= total no. of the data

17. Linear interpolation Steps in interpolation method 1. Arrange the scores in ascending order 2. Locate the position of the score in the distribution 3. Since the result is in decimal number, proceed to linear interpolation 4. Find the difference between the two values wherein Q1 is situated 5. Multiply the result in step 2 by the decimal part obtained in step 4 6. Add the result in step 5 to the second smaller number in step 4

18. Linear interpolation Example: Find the first quartile (Q1), and the third quartile (Q3), Given the scores of 9 students in their mathematics activity using linear interpolation {1, 27, 16, 7, 31, 7, 30, 3, 21 }

19. Linear interpolation Step 1 : Arrange the scores in ascending order { 1, 3, 7, 7, 16, 21, 27, 30, 31 } Step 2: Locate the position of the score in the distribution Position of Q1= ¼(n+1) Q1= ¼ (9+1) Q1= 0.25(10) Q1= 2.5

20. Linear interpolation Step 3: Since the result is in decimal number, proceed to linear interpolation Step 4: Find the difference between the two values wherein Q1 is situated { 1, 3, 7, 7, 16, 21, 27, 30, 31 } 2.5 position Q1 is between the values 3 and 7, therefore = 7-3 = 4

21. Linear interpolation Step 5: Multiply the result in step 2 by the decimal part obtained in step 4 = 4 (0.5) = 2 Step 6: Add the result in step 5 to the second smaller number in step 4 = 2+3 = 5 Therefore the value of Q1 is equal to 5