Calculatingmeasures of position of grouped data.help me please. The references is on what is it

the yalu as of lower that follOWsWrite'yo 2;th '3'on your answer sheet. Filled. In (cf) and answer the questions - 'C. independent Ac ' Directions: Copy . and cumulative frequency answer sheet. . . ' ' ' I '3' Math Class Table 3; H " 1. What lower boundary is considered in solving for the 30'\" percentile? 2. What is the cumulative frequency to be used in solving for the 8m deciie? " 3. At what class interval the 1" quartile is contained? 4. if we have to solve for the 50'" percentile, what is its class freqUency (fpso)? 5. What is the value of the 4m decile? D. Independent Assessment 2 , , Directions: Refer to table 4 to answer the questions below. Write only the letter of the correct answer on your answer sheet. TABLE 4 Lower Boundaries (LB) 1.:Which lower boundary is considered in solving for the 40'h percentile? A. 20.5 8.25.5 ~ ~ 0. 30.5 ' D as 5 2 an? cumulative frecutzqcy shall be used to solve for the 5'h decrle? 3. What is the 2"d quartile in the given set of data? ' 28 A. 26 B. 26.5 C. 30' _ D '30 5 4. Which of the following is the value of the 4m decile'? ' ' A. 24.07 e. 24.87 c. 26.07. b 26 37 - I5..Wh"at is the measure of the 60"1 percentile? . A. 27.05. . .. 3.27.5 C. 28.05 _, D. 23 ,5 . _ 5. How many students took the test? D. 50 A. 36 B. 40 C. 45 2 6. Which lower boundary is considered in solving for the 70th percentile? D. 35.5 A. 20.5 B. 25.5 C. 30.5 7. What cumulative frequency shall be used to solve for the 2nd quartile? A. 45 B. 40 C. 25 D. 16 8. What is the 1 quartile of the given set of data? D. 21.07 A. 25.72 B. 24.00 C. 22.53 9. Which of the following is the value of the 4th decile? A. 28.50 B. 26.61 C. 20.50 D. 18.00 10. What is the measure of 80 percentile? A. 34.16 B. 32.14 C. 25.12 D. 15.10 What's In Recall: Measures of Position: Quartiles are values that divide a set of data into 4 equal groups. There are 3 quartiles, denoted by Q1, Qz, and Qs. In this organization of data, twenty-five percent (25%) of the distribution falls below the first quartile, fifty percent (50%) falls below the second quartile, seventy-five percent (75%) falls below the third quartile, while 25% will be equal or greater than the third quartile. Deciles are values that divide a set of data into 10 equal groups. There are 9 deciles, denoted by D1, falls below De. D2, Ds, ..., De. In this organization of data, 10% falls below D1, 20% falls below D2, and so on, and 90% Percentiles are values that divide a set of data into 100 equal groups. There are 99 percentiles denoted by P1, P2, Ps, ..., Pos. In this organization of data, 1% falls below P1, 2% falls below P2, and so on, and 99% falls below Pog. Formulas for finding the measures of position of ungrouped data: QUARTILE DECILE Qx= (n + 1) D = 4 To (n + 1) PERCENTILE = 100 (n + 1) Quartile has a divisor of 4 as the data in QUARTILES are divided into 4 equal groups. Decile has a divisor of 10 as the data in DECILES are divided equally into 10 equal groups. groups. Percentile has the divisor of 100 as the data in PERCENTILES are divided equally into 100 equalWhat's New Task 1. What is the 3"d quartile of the given set of data in the table below? Lower Cumulative Class Interval Frequency (f) Boundaries Frequency of the Scores (LB) (cf) 31- 35 4 26- 30 12 21- 25 15 16-20 7 11- 15 4 6- 10 3 . Are you going to use the same procedure in finding the Measures of Position of ungrouped data? Why? . What are the data needed to calculate the 3d quartile of the given grouped data in the table? . How are the values of the lower boundaries (LB) and cumulative frequency (cf) in the table be solved? Task 2. What is the 4th decile of the given grouped of data? Lower Cumulative Class Interval Frequency Boundaries Frequency of the Scores (f) LB) (cf) 22 - 24 4 21.5 45 19 - 21 12 18.5 41 16 - 18 15 15.5 29 13 - 15 7 12.5 14 10 - 12 4 9.5 7 7- 9 3 6.5 3 i = 3 N = 45 Task 3. Calculate the 20th Percentile (P20) of the data presented. Class Interval Frequency Lower Cumulative of the Scores (f) Boundaries Frequency (LB 22 - 24 (cf) 4 21.5 45 19 - 21 12 18.5 16 - 18 41 15 15.5 13 - 15 29 7 12.5 10 - 12 14 4 7- 9 9.5 3 7 6.5 1 = 3 3 N = 454 What is it? To calculate the Measures of Position of grouped data, the following formulas are used: PERCENTILE DECILE QUARTILE 100)-of b DK=LB + 10) -FB PK = LB + fPK QKELB+ fDK fok where: Px = the kth percentile 2x =the kth quartile; DK = the kth decile; k = nth percentile K= nth quartile, k = nth decile n = 1, 2, or 3 n = 1, 2, ..., or 9 n = 1, 2, ..., or 99 LB = lower boundary of the kth class N = total frequency Cfo = cumulative frequency of the class before the kth class fx = frequency of the kth class i = size of class interval To solve the Measures of Position of grouped data using the given formulas, we need to have the values of the indicated variables first, as well as the class interval of the kth position where the score is contained. Let us consider the given tasks. Task 1. What is the 3'd quartile of the given set of data in the table below? Class Interval of the Frequency (f) Lower Cumulative Scores Boundaries (LB) Frequency 31-35 (cf) 4 26-30 12 21- 25 15 16-20 7 11-15 4 6- 10 3 Solution: frequency (cf). Step 1. Complete the table by filling up the values of lower boundaries (LB) and Cumulative lower limit. The lower boundaries of each class are calculated by subtracting 0.5 from the class The lower limit for every class is the smallest value in that class. Cumulative Frequency is obtained by adding each frequency from a frequency distribution value of N. to the running total. The last value is always equal to the total for all observations or theSolution Table 5 Cumulative Frequency Class Interval of | Frequency Lower Boundaries (LB) (cf) the Scores (f) 41+ 4 = 45 22 - 24 4 22 - 0.5 = 21.5 29 + 12 = 41 19 - 21 12 19 - 0.5 = 18.5 14 + 15 = 29 16 - 18 15 16 - 0.5 = 15.5 7 +7 = 14 13 - 15 13 - 0.5 = 12.5 3+4=7 10 - 12 10- 0.5 = 9.5 3 7- 9 3 7 -0.5 = 6.5 Final Table of Values Lower Boundaries (LB) Cumulative Frequency Class Interval of Frequency (cf) he Scores (f) 21.5 45 22 - 24 4 19 - 21 12 18.5 41 16 - 18 15 15.5 29 14 13 - 15 7 12.5 7 10 - 12 4 9.5 3 7- 9 3 6.5 1 = 3. N = 45 Step 2.Identify the class interval of the kth position where the score is obtained. Class Interval of the 3'd quartile (Q3). Q3 Class: N = = (45) = 135 135 = 33.75 . The numerator is 3 because it is Q3. The denominator is 4 because quartiles divide the data into 4 equal groups. The value of N is 45 because the total frequency is 45 >Q3 class is 33.75. This means you need to find the class interval where the 33.75th score contained. Refer to the Cumulative Frequency Column. Identify at what class interval, 33.75th score included. Note that the 30th - 41st scores belong to the class interval: 19 - 21. So, the 33.75th score is also within this class interval. Class Frequency Lower Cumulative Interval of (f) Boundarie Frequency the Scores S (LB) (cf) 22 - 24 4 21.5 19 - 21 45 12 18.5 16 - 18 15 41 (30th .- 41" score) 15.5 + Q3 class 13 - 15 29 7 + Cf. (cumulative frequen 10 - 12 12.5 14: A 7- 9 9.5 3 7 of the class before 6.5 3 ha the Q3 class) 1 = 3 N = 45 Grade 10 MathemStep 3. Identify the formula and the data needed, then solve for Q3. 6 The formula is: Where: LB = 18.5 K = 3 QK = LB+ eli N = 45 for Cfb = 29 fQ3 = 12 i = 3 KN _ 3(45) = 34 QK = L8+ fox Q3 = 18.5 + 34 -29 3 (Substitution) 12 Q3 = 18.5 + 3 (Subtract 29 from 34.) Q3 = 18.5 + 1.25 (Divide 15 by 12 up to 2 decimal places.) Q3 = 19.75 (Add 18.5 and 1.25.) The 3'd quartile is 19.75 Task 2. What is the 4th decile of the given group of data? Frequency Lower Cumulative Class Interval Boundaries Frequency of the Scores (f) (LB) (cf) 22 - 24 4 21.5 45 19 - 21 12 18.5 41 16 - 18 15 15.5 29 13 - 15 7 12.5 14 10 - 12 4 9.5 7 7- 9 3 6.5 3 i = 3 N = 45 Solution: The lower boundaries and cumulative frequency are given, we will proceed to step 2, identifying the class interval of the kth position where the score is obtained. Step 2. Identify the class interval of the 4th decile (D4). D4 Class: * N = (45) = 18 The numerator is 4 because it is D4. The denominator is 10 because deciles divide the data into 10 equal groups. The value of N is 45 because the total frequency is 45 D4 class is 18. This means you need to find the class interval where the 18th score is contained. Refer to the Cumulative Frequency Column. Identify at what class interval, 18th score is included. Note that the 15th - 29th scores belong to the class interval: 16 - 18. So, the 18th score is also within this class interval.Class Interval Frequency Lower Cumulative of the Scores (f) Boundaries Frequency LB) (cf) 22 - 24 4 21.5 45 19 - 21 12 18.5 41 16 - 18 15.5 29 (15th . 29th score D4 class 15 13 -15 Cfi, (cumulative 7 12.5 14 10 - 12 7 frequency of the 9.5 7- 9 6.5 3 class before the D4 class). i = 3 N = 45 Step 3. identify the formula and the data needed, then solve for D4. The formula is: Where: LB = 15.5 K = 4 DK = LB + N = 45 fDK Cfo = 14 fD4 = 15 I = 3 DK = LB + 10)-CFB KN 4(45) 2 = 18 10 10 fDK [18 -14 3 D4 = 15.5 + 15 (Substitution) D4 = 15.5 + 3 (Subtract 14 from 18.) D4 = 15.5 + 0.8 (Divide 12 by 15.) BA D4 = 16.3 (Add 15.5 and 0.8.) The 4th decile is 16.3 Task 3. Calculate the 20th Percentile (P20) of the data presented. Lower Class Interval Frequency Cumulative of the Scores (f ) Boundaries Frequency (LB) (cf) 22 - 24 4 21.5 45 19 - 21 12 18.5 41 16 - 18 15 15.5 29 13 - 15 7 12.5 14 10 - 12 4 9.5 7 7- 9 3 6.5 3 i = 3 N = 45 Solution: The lower boundaries and cumulative frequency are given, let us proceed to step 2, identifying the class interval of the kth position where the score is obtained.Step 2. Identify the class interval of the 20th percentile (P20). P20 Class: 20 N = 100 (45) = 9 100 The numerator is 20 because it is P 20. The denominator is 100 because percentiles divide the data into 100 equal groups. N = 45 because the total frequency is 45 DP20 class is 9. This means you need to find the class interval where the 9th score is contained Refer to the Cumulative Frequency Column. Identify at what class interval, 9th score is included. Note that the 8th - 14th scores belong to the class interval: 13 - 15. So, the 9th score is also within this class interval Lower Cumulative Class Interval Frequency Boundaries (LB) Frequency of the Scores (f) (cf) 22 - 24 4 21.5 45 19 - 21 12 18.5 41 16 - 18 15 15.5 29 13 - 15 7 12.5 14 ( 8th - 14th score) +- P20 class 10 - 12 4 9.5 7 - Cfo (cumulative 7- 9 3 6.5 3 frequency of the class before the P20 class) i = 3 N = 45 Step 3. Identify the formula and the data needed, then solve for P20. The formula is: Where: LB = 12.5 K = 20 KN PK = LB + 100)-cf b N = 45 fPK Cfo = 7 fp20) = 7 i = 3 PK = LB+ 100 -cf b KN 20(45) 10 0 10 fPK P20 = 12.5 + 27/3 (Substitution) P20 = 12.5 + $3 (Subtract 7 from 9.) P20 = 12.5 + 0.86 (Divide 6 by 7 then round it up to 2 decimal places.) P20 = 13.36 (Add 12.5 and 0.86.) The value of the 20th quartile is 13.36What's More A. Independent Activity 1 Directions: Copy table 1 on your answer sheet and derive the values of the lower boundaries (LB) and cumulative frequencies (cf). TABLE 1 Lower Cumulative Boundaries Frequency Class Interval Frequency (f) (LB) (cf) 31-35 5 26-30 7 21- 25 9 16-20 4 11- 15 3 B. Independent Assessment 1 Directions: Refer to table 2 to answer the questions below. Write only the letter of the correct answer on your answer sheet. TABLE 2 Lower Cumulative Frequency Class Interval of the Scores Frequency (f) Boundaries (LB) (cf) 36- 40 35.5 40 31-35 8 30.5 36 26-30 10 25.5 28 21- 25 7 20.5 18 16-20 6 15.5 11 11-15 3 10.5 5 6- 10 2 5.5 2 1. What is the class interval of the data shown in the table? A. 2 B. 3 C. 5 D. 7 2. How many students got a score of 25 and below? A.6 B. 11 C. 18 D. 36 3. What is the cumulative frequency for the class of 21 - 25? A. 11 B. 18 C. 28 D. 36 4. How many students took the test? A. 40 3. 36 C. 35 D. 31 5. What is the cumulative frequency before the 31 - 35 class interval? A. 8 B. 10 C. 28 D. 36Calculating Med What I Know Directions: Find out how much you already know about the content of this module. Write the letter that corresponds to your answer on a separate answer sheet. Take note of the items that you were not able to answer correctly and find the right solution as you go through this module. 1. Which of the following is the grouped frequency distribution of the ages of 25 randomly selected college students of Sugbo University, if the ages are as follows: 17, 18, 19, 36, 20, 37, 21, 18, 44, 22, 18, 25, 29, 48, 24, 19, 30, 27, 18, 36, 20, 36, 52, 21, 22? C D 20 & below 9 20 & below 9 20 & below 20 & below 9 21- 30 21-30 21- 30 21- 30 8 31-40 31- 40 31-40 3 31- 40 4 41-50 2 41-50 2 41- 50 3 41-50 2 Over 50 1 Over 50 1 Over 50 1 Over 50 2 For items number 2-4, refer to the table below that shows the number of hours worked by 200 statistics students to accomplish their statistical mini-research. Number of Hours Frequency 40 - 49 40 2. What is the class interval of the data shown in the table? B. 10 C. 11 D. varies from class to class 30 - 39 50 A. 9 20 - 29 70 3. How many students worked for 19 hours or less? 10 - 19 40 A. 40 B. 50 C. 70 D. cannot be determined 4. What is the cumulative frequency for the class of 20 - 29? A. 40 B. 50 C. 70 D. 110 For items number 5 -10, refer to the data shown in the table Scores Frequency (f) Lower Boundaries Cumulative Frequency . .. (LB) (cf) 36 - 40 5 35.5 45 31 - 35 15 30.5 40 26 - 30 9 25.5 25 21 - 25 8 20.5 16 16 - 20 6 15.5 8 11 - 15 N 10.5 2