a powerpoint presentation on illustrating measure of position

a powerpoint presentation of ungrouped data, quartiles, deciles, percentiles

1. Find the median of the following set of data. 1. 4, 7, 1, 8, 10 2. 8, 6, 6, 10, 85 3. 34, 43, 45, 1, 30, 4 4. 29, 3, 42, 17, 17, 48, 7 5. 45, 47, 2, 44, 42, 27

2. How did you find the median of the set of data? ➢ To find the median : 1. Arrange the numbers from smallest to largest. 2. The number in the middle is the median. If there are two middle numbers, add them and divide by two. The median divides the distribution into two equal parts. It is a point of distribution where one-half of the distribution lies below it or above it.

3. MEASURE OF POSITION A measure of position is a statistical method that determines the position of a data value within a set of data. It can also be used to compare data values across different sets.  Ways to find measure of position for ungrouped data General method Mendenhall and Sincich Method Linear Interpolation

4. The Quartiles of Ungrouped Data The QUARTILES are the score points which divide a distribution into four equal parts. The difference between and is the interquartile range .  

5. Since the second quartile is equal to the median, the steps in the computation of median by identifying the median class is the same as the steps in identifying the Q1 class and the Q3 class. Q1 Q2 Q3 a.25% of the data has a value ≤Q1 b.50% of the data has a value ≤Q2 c.75% of the data has a value ≤Q3

6. Example 1: The owner of a 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. Find the lower quartile and upper quartile of the data. Example 2: Consider the set of scores in Math 10 of Section Rizal: 11, 13, 14, 15, 15, 16, 19, 19, 20. Find  

7. The Dec iles of Ungrouped Data The DECILES are the score points which divide a distribution into ten equal parts . =   If the quotient obtained is NOT a whole number, round to the next larger whole number

8. Example: Ms. Dela Cruz is a Mathematics Teacher, she gives a 60-item test for remedial class. The scores of fifteen students are 20,35, 55, 28, 46, 32, 25, 56, 55, 28, 37, 60, 47, 17, 52. Find the value of the 2 nd decile, 7 th decile, and 8 th decile .

9. The PERCENTILES are the score points which divide a distribution into 100 equal parts . =   If the quotient obtained is NOT a whole number, round to the next larger whole number The Percenti les of Ungrouped Data

10. Examples: The list shows the number of bottles of strawberry jam sold in a day by 14 different vendors: 20, 18, 16, 10, 12, 15, 13,9, 11, 16, 15, 16, 18, 20

11. Mendenhall and Sincich Method Lower Quartile (L) = Position of =   If L falls halfway between two integers, round up. The Lth element is the lower quartile ( . Upper Quartile (U) = Position of = If U falls halfway between two integers, round down. The Uth element is the upper quartile ( .   Example 3: Given the set of data: 1, 3, 7, 7, 16, 21, 27, 30, 31 Find and .  

12. Linear Interpolation  A method of finding the quartile value. We need to use the interpolation if the value of the position is in decimal form. Using the formula = (n+1) k= position of the quartile n= total no. of the data  

13. Steps in Linear interpolation Method  Arrange the scores in ascending order Locate the position of the score in the distribution Since the result is in decimal number, proceed to linear interpolation Find the difference between the two values wherein Q1 is situated Multiply the result in step 2 by the decimal part obtained in step 4 Add the result in step 5 to the second smaller number in step 4. Example 3: Given the set of data: 1, 3, 7, 7, 16, 21, 27, 30, 31 Find and by linear interpolation.