ETUlay Online Tutorial Math 10 Quarter 4 - Week 1-2 Measures of Position of Ungrouped Data depedetulay β’DepED – Cordillera Administrative Region β’SDO - Camarines Sur Q4 W2 Math 10 At the end of the session, you will be able to: β’ calculate a specified measure of position th (e.g. 90 percentile) of a set of data; and β’ solve problems involving measures of position. Q4 W2 Math 10 W1 Math Tukey’s Method Averina, a shoe store owner, wanted to compare the different brands of shoes. The table below shows her record of the number of pairs of shoes bought from each of the brands in one week. Find π1, π2, π3. 107, 128, 137, 138, 141, 142, 151, 209 Mathletes! Are you now ready? Let’s get started! #MATHibay Q4 W2 Math 10 1. It is a measure by which the position of a data is determined through its value. a. quartile b. c. percentile d. measures of position Q4 W2 Math 10 decile 2. What measure divides the distribution into ten equal parts? a. quartile b. c. percentile d. measures of position Q4 W2 Math 10 decile 3. Which of the following does NOT belong in the group? a. nd 2 quartile c. th 5 decile Q4 W2 Math 10 b. nd 2 decile d. th 50 percentile MATH I Have Learned Measures of Position QUARTILE DECIILE PERCENTILE Divides the distribution into 4 equal parts Divides the distribution into 10 equal parts Divides the distribution into 100 equal parts Ungrouped Data π πΈπ = (π + π) π Q4 W2 Math 10 π π«π = (π + π) ππ π π·π = (π + π) πππ Measures of Position When the position is in decimal number, we have two methods in determining the exact position. Mendenhall and Sincich Method Interpolation Q4 W2 Math 10 Quartiles of Ungrouped Data 3.4 3.6 4 4 ππ% ππ% ππ% πΈπ πΈπ πΈπ ROUND UP π πΈπ = (π + π) π Q4 W2 Math 10 ROUND DOWN ππ π(π + π) πΈπ = π 7.4 7.6 7 7 Deciles of Ungrouped Data 10% 20% 30% 40% 50% 60% 70% 80% 90% π«π π«π π«π π«π π«π π«π π«π π«π π«π 4.3 ROUND UP 5 π π«π = (π + π) ππ Q4 W2 Math 10 ROUND DOWN ππ π(π + π) π«π = ππ 8.7 8 Percentiles of Ungrouped Data 10% 20% 30% 40% 50% 60% 70% 80% 90% π·ππ π·ππ π·ππ π·ππ π·ππ π·ππΆ π·ππ π·ππ π·ππ 2.8 ROUND UP 3 π π·π = (π + π) πππ Q4 W2 Math 10 ROUND DOWN ππ π(π + π) π·π = πππ 12.5 12 Quartiles of Ungrouped Data Calculate the lower quartile(Q1) and upper quartile(Q3) of the data. The number of days taken by each of 13 employees to finish a job were 32, 27, 39, 27, 23, 35, 42, 42, 29, 46, 37, 42, and 35. πΊππππππππ: 1. Arrange the values in ascending order. 23 27 27 29 32 35 35 37 39 42 42 42 46 π 2. Locate the positions of πΈπ and πΈπ using the formula πΈπ = (π + π). π Note: π is the number of data elements. Thus, π = ππ. Q4 W2 Math 10 Measures of Position for Ungrouped Data Mendenhall and Sincich Method π 2. Locate the positions of πΈπ and πΈπ using the formula πΈπ = (π + π). πΊππππππππ: π Note: π is the number of data elements. Thus, π = ππ. π πΈπ = (π + π) π π πΈπ = (ππ + π) π π πΈπ = (ππ) π πΈπ = π. π Q4 W2 Math 10 π πΈπ = (π + π) π π πΈπ = (ππ + π) π π πΈπ = (ππ) π πΈπ = ππ. π Measures of Position for Ungrouped Data Mendenhall and Sincich Method π 2. Locate the positions of πΈπ and πΈπ using the formula πΈπ = (π + π). πΊππππππππ: π Note: π is the number of data elements. Thus, π = ππ. Q4 W2 Math 10 π πΈπ = (π + π) π π πΈπ = (π + π) π πΈπ = π. ππ(ππ + π) πΈπ = π. ππ(ππ + π) πΈπ = π. ππ(ππ) πΈπ = π. ππ(ππ) πΈπ = π. π πΈπ = ππ. π Measures of Position for Ungrouped Data 4π‘β πΊππππππππ: 10π‘β 23 27 27 29 32 35 35 37 39 42 42 42 46 πΈπ = π. π πΈπ πΈπ = ππ. π ROUND UP ROUND DOWN ππ =π ππ πΈπ πΈπ = ππ The lower quartile value is the 4th data element. The upper quartile value is the 10th data element. ∴ The value of πΈπ is 29. ∴ The value of πΈπ is 42. Q4 W2 Math 10 Mendenhall and Sincich Method Measures of Position for Ungrouped Data 8π‘β π¬ππππππ: 23 27 27 29 32 35 35 37 39 42 42 42 46 Find the 6th decile of the given data. π π«π = (π + π) ππ π π«π = (ππ + π) ππ ROUND DOWN π«π = π. ππ(ππ) The 6th decile value is the 8th data element. π«π = π. π Q4 W2 Math 10 π«π = π ππ ∴ The value of π«π is 37. Measures of Position for Ungrouped Data 5π‘β π¬ππππππ: 23 27 27 29 32 35 35 37 39 42 42 42 46 Find the 32nd percentile of the given data. π π·π = (π + π) πππ ππ π·ππ = (ππ + π) πππ π·ππ = π. ππ(ππ) π·ππ = π. ππ Q4 W2 Math 10 ROUND UP π·ππ = π ππ The 32nd percentile value is the 5th data element. ∴ The value of π·ππ is 32. Measures of Position for Ungrouped Data Interpolation 23 27 27 29 32 35 35 37 39 42 42 42 46 πΊπππππππ: Position of πΈπ = π. π rd th (3.5 falls between 3 and 4 data) 1. Subtract the 3rd data from the 4th data. ππ − ππ = π 2. Multiply the result by the decimal part obtained in the position of πΈπ . π. π π = π 3. Add the result in the 3rd data. π + ππ = ππ Q4 W2 Math 10 ∴ The value of πΈπ using interpolation is 28. Measures of Position for Ungrouped Data Interpolation 23 27 27 29 32 35 35 37 39 42 42 42 46 πΊπππππππ: Position of π«π = π. π th th (8.4 falls between 8 and 9 data) 1. Subtract the 9th data from the 8th data. ππ − ππ = π 2. Multiply the result by the decimal part obtained in the position of π«π . π. π π = π. π 3. Add the result in the 8th data. π. π + ππ = ππ. π ∴ The value of π«π using interpolation is 37.8. Q4 W2 Math 10 Measures of Position for Ungrouped Data Interpolation 23 27 27 29 32 35 35 37 39 42 42 42 46 πΊπππππππ: Position of π·ππ = π. ππ th th (π. ππ falls between 4 and 5 data) 1. Subtract the 4th data from the 5th data. ππ − ππ = π 2. Multiply the result by the decimal part obtained in the position of π·ππ . π. ππ π = π. ππ 3. Add the result in the 4th data. π. ππ + ππ = ππ. ππ ∴ The value of π·ππ using interpolation is 30.44 Q4 W2 Math 10 Mathletes! Are you now ready to take the Quick Check Challenge of the Week? #MATHibay Q4 W2 Math 10 Mr. Ling is an English teacher. He is interested in the reading speed of his students. The following are the numbers of words his students can read in one minute: 50, 25, 23, 30, 42, 20, 13, 16,16, 10, 12, 11, 11, 11, and 19. 10 11 11 11 12 13 16 16 19 20 23 25 30 42 50 1. Find the 1st quartile of the given data. π πΈπ = (π + π) π π πΈπ = (ππ + π) π π πΈπ = (ππ) π Q4 W2 Math πΈπ =10π The 1st quartile value is the 4th data element. ∴ The value of πΈπ is 11. Mr. Ling is an English teacher. He is interested in the reading speed of his students. The following are the numbers of words his students can read in one minute: 50, 25, 23, 30, 42, 20, 13, 16,16, 10, 12, 11, 11, 11, and 19. 10 11 11 11 12 13 16 16 19 20 23 25 30 42 50 2. Find the 8th decile of the given data. π π«π = (π + π) ππ π π«π = (ππ + π) ππ π«π = π. π(ππ) ππ. π Q4 W2π« Math π = 10 ROUND DOWN π«π ππ = ππ The 8th decile value is the 12th data element. ∴ The value of π«π is 25. Measures of Position for Ungrouped Data 3. Find the 8th decile of the given data using interpolation. 10 11 11 11 12 13 16 16 19 20 23 25 30 42 50 Position of π«π = ππ. π th th (12.8 falls between 12 and 13 data) 1. Subtract the 13th data from the 12th data. ππ − ππ = π 2. Multiply the result by the decimal part obtained in the position of π«π . π. π π = π 3. Add the result in the 12th data. π + ππ = ππ ∴ The value of π«π using interpolation is 29. Mathletes! Are you now ready to take the Math Challenge of the Week? #MATHibay Q4 W2 Math 10 The scores of Mr. Math Wizard candidate from the five judges were recorded as follows: 93, 92, 88, 86, and 90. a. Find π1 , D3, and P10 using Mendenhall and Sincich Method. Q4 W2 Math 10
