Q4_Week1_Measures of Position(ungrouped data).pptx

It discusses about the measures of positions for ungrouped data. It shows how to solve for quartiles, deciles and percentiles. It gives examples for each quantiles. Showing step-by-step procedures including the Linear Interpolation.

1. THE PROBABILITY CIPHER Probability of drawing a red card OR a face card from a standard deck. Probability that the sum of two dice is at least 10. Mariel has 24 different colored balls in a jar. 8 of these balls are green, 6 are orange, and 10 are violet. What is the probability that Mariel draws a ball that is either green or not violet Probability of flipping tails AND rolling an odd number on a six-sided die. A letter is randomly chosen from the word “MATHEMATICS”. Find the probability that a letter A or T is selected.

2. Probability that a randomly selected student from a group of 30 (where 12 play soccer, 15 play basketball, and 6 play both) plays at least one sport. Probability of spinning an even number OR a number greater than 5 on an 8-section spinner. Probability of rolling two dice and getting a sum of AT LEAST 12. Probability of drawing two green balls from a bag of 4 red, 6 blue, and 10 green balls (without replacement). Probability of drawing a queen or a heart from a standard deck of 52 cards.

3. MATHEMATICS 10 Week 1 Measures of Position by: SHARON A. MIRANDA

4. Illustrates the following measures of position: quartiles, deciles and percentiles. Calculates a specified measure of position (e.g. 90th percentile) of a set of data.

5. BACKGROUND: The term “ STATISTICS ” is a branch of Mathematics that deals with the collection , organization , presentation , analysis , and interpretation of data . It is a field of study which deals with mathematical characterization of a group or groups of items.

6. NATURE OF DATA QUALITATIVE DATA - is the descriptive and conceptual findings collected; non-numeric data QUANTITATIVE DATA - refers to any data that can be quantified; numeric data

7. QUANTITATIVE DATA Discrete data result from either a finite number of possible values or countable number of possible values as 0 or 1, or 2, and so on. Continuous data result from infinitely many possible values that can be associated with points on a continuous scale in such a way that there are no gaps or interruptions.

8. Another way to classify data is to use four levels of measurements: Nominal level of measurement is characterized by data that consist of names, labels or categories only. Ordinal level of measurement involves data that may be arranged in some order but differences between data values either cannot be determined or are meaningless.

9. Another way to classify data is to use four levels of measurements: Interval level of measurement has no inherent (natural) zero starting point (where none of the quantity is present) Ratio level of measurement is the interval level modified to include the inherent zero starting point (where zero indicates that none of the quantity is present)

10. BACKGROUND: Collection of data refers to the process of gathering numerical information. This includes interview , questionnaire , experiments , observation and documentary analysis .

11. BACKGROUND: Once the data are gathered, the next step in statistical inquiry is the presentation of data in appropriate tables and graphs. Such tables refer to frequency distribution which may either be one-dimensional or two dimensional. Graphical presentation includes bar graphs , frequency polygon , pie graph and many others .

12. BACKGROUND: Analysis of data refers to the activity of describing the properties or behavior of the data or the possible correlation of different quantities or variables.

13. BACKGROUND: Finally, interpretation has to be made based on the preliminary activities and other statistical methods. Such methods involve testing the significance of the results.

14. Descriptive statistics allow you to characterize your data based on its properties. There are four major types of descriptive statistics: 1. Measures of Frequency : * Count, Percent, Frequency * Shows how often something occurs * Use this when you want to show how often a response is given

15. 2. Measures of Central Tendency * Mean, Median, and Mode * Locates the distribution by various  points *  Use this when you want to show how an average or most commonly indicated response

16. 3. Measures of Dispersion or Variation * Range, Variance, Standard Deviation * Identifies the spread of scores by stating intervals * Range = High/Low points * Variance or Standard Deviation = difference between observed score and mean * Use this when you want to show how "spread out" the data are. It is helpful to know when your data are so spread out that it affects the mean

17. 4. Measures of Position * Percentile Ranks, Quartile Ranks * Describes how scores fall in relation to one another. Relies on standardized scores * Use this when you need to compare scores to a normalized score (e.g., a national norm)

18. Measures of Position (Ungrouped Data)

19. When the set of data is arranged from lowest to highest, the distribution can be divided into two , four , ten , or hundred equal parts. The points that divide the set of data equally are called quantiles .

20. As you can see, Quartile 2 is equivalent to Decile 5 , also in Percentile 50 , and also to Median . Aside from that, Decile 1 is equivalent to Percentile 10 . Quartile 1 is equivalent to Percentile 25.

21. Finding the Measures of Position (ungrouped data)

22. Given the data below: Scores of selected students of G10 – Magdalo in a 20-item Mathematics test 12 13 11 10 15 16 14 17 20 9 Find the following: a. Percentile 50 b. Decile 5 c. Quartile 2

23. Before the computation, first we must ARRANGE the data from lowest to highest. 9, 10, 11, 12, 13, 14, 15, 16, 17, 20

24. To get the formula of Percentile 50, We all know that the distribution of Percentile is divided by 100, so the formula would be…   Where: P – Percentile N – number of data K – position of the data

25. a. Find the Percentile 50 n = 10 (since there are 10 data) k = 50 9, 10, 11, 12, 13, 14, 15, 16, 17, 20   Solution:       5 th data   5 th data

26. To get the formula of Decile 5, We all know that the distribution of Decile is divided by 10, so the formula would be…   Where: D – Decile N – number of data K – position of the data

27. Find Decile 5 n = 10 (since there are 10 data) k = 5 9, 10, 11, 12, 13, 14, 15, 16, 17, 20   Solution:       5 th data   5 th data Same value as of percentile 50, this signifies that decile 5 and percentile 50 are equal or the same.

28. To get the formula of Quartile 2 , We all know that the distribution of Quartile is divided into 4, so the formula would be…   Where: Q – Quart ile N – number of data K – position of the data

29. Find Quartile 2 n = 10 (since there are 10 data) k = 2 9, 10, 11, 12, 13, 14, 15, 16, 17, 20   Solution:       5 th data   5 th data Same value as of percentile 50 and decile 5, this signifies that decile 5 and percentile 50 are equal to quartile 2.

30. General Point Average in Mathematics of selected Grade 10 students: 77 83 76 85 80 95 91 75 89 81 79 80 87 78 78 80 90 88 92 81

31. Arrange the data in ascending order. 75 76 77 78 78 79 80 80 80 81 81 83 85 87 88 89 90 91 92 95

32. a . Find   75 76 77 78 78 79 80 80 80 81 81 83 85 87 88 89 90 91 92 95 Solution:         10 th data   This means that 50% of the data is less than or equal to 81 .

33. b . Find   75 76 77 78 78 79 80 80 80 81 81 83 85 87 88 89 90 91 92 95 Solution:         6 th data   This means that 3 0% of the data is less than or equal to 79.

34. c . Find   75 76 77 78 78 79 80 80 80 81 81 83 85 87 88 89 90 91 92 95 Solution:         16 th data   This means that 80% of the data is less than or equal to 89.

35. d . Find   75 76 77 78 78 79 80 80 80 81 81 83 85 87 88 89 90 91 92 95 Solution:         15 th data   This means that 75 % of the data is less than or equal to 88 .

36. e . Find   75 76 77 78 78 79 80 80 80 81 81 83 85 87 88 89 90 91 92 95 Solution:         14 th data   This means that 70% of the data is less than or equal to 87 .

37. f . Find   75 76 77 78 78 79 80 80 80 81 81 83 85 87 88 89 90 91 92 95 Solution:         18 th data   This means that 88% of the data is less than or equal to 91 .

38. f . Find   75 76 77 78 78 79 80 80 80 81 81 83 85 87 88 89 90 91 92 95 Solution:       Since the answer is decimal number, we can use linear interpolation.

39. f . Find   75 76 77 78 78 79 80 80 80 81 81 83 85 87 88 89 90 91 92 95 Solution:     Steps: 1. Find the value of the nth position and the nth+1 position. 17 th position 18 th position 2. Find the difference between the two values. 17 th position= 90 18 th position= 91 91 – 90 = 1

40. Solution:   Steps: 1. Find the value of the nth position and the nth+1 position. 2. Find the difference between the two values. 17 th position= 90 18 th position= 91 91 – 90 = 1 3. Multiply the difference by the decimal part you get in solving the percentile. f . Find     1 x 0.6= 0.6 4. Add the product to the lowest value in step 1. 0.6 + 90= 90.6  

41. a . Find   45 40 52 49 48 42 49 47 40 41 39 36 44 35 36 Given the following weight (in kilo) of 15 Grade 10 students, use linear interpolation to solve the following measures of position. b . Find  

42. a . Find         Arrange the data in ascending order. 35 36 36 39 40 40 41 42 44 45 47 49 49 50 52 3 rd & 4 th position Solution:   Step 1: 3 rd position= 36 4 th position= 39 Step 2: 39 – 36 = 3 Step 3: 3 x 0.75= 2.25 Step 4: 2.25 + 36= 38.25  

43. b . Find         Arrange the data in ascending order. 35 36 36 39 40 40 41 42 44 45 47 49 49 50 52 11 th & 12 th position Solution:   Step 1: 11 t h position= 47 12 th position= 49 Step 2: 49 – 47 = 2 Step 3: 2 x 0.25= 0.5 Step 4: 0.5 + 47= 47.5  

44. LEARNING TASK 1 (WEEK 1) Quartiles Deciles Percentiles  1 ?  2 ?  ?  5 ? 3   ?   ?  60  7  ? 9 ? ? 10 ? Fill in the box with its corresponding equivalent measures of position.

45. Compute the following, given the: Distribution of Age of selected residence in Brgy . Hugo Perez, Trece Martires City, Cavite. 11 12 16 30 45 50 51 45 23 27 34 37 31 28 49 18 41 48 55 60 (Note: Arrange the data from Lowest to Highest) Find the following: a. Quartile 1 b. Percentile 75 LEARNING TASK 2 (WEEK 1)